AP Physics Circular Motion and Rotation 2 nd

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AP Physics Circular Motion and Rotation 2 nd SEMESTER, Unit 5 -2 Dr. Crofoot

AP Physics Circular Motion and Rotation 2 nd SEMESTER, Unit 5 -2 Dr. Crofoot RIM High School

Circular Motion and Rotation 02/25/20 Starter/Plicker A wheel with an angular inertia of 56

Circular Motion and Rotation 02/25/20 Starter/Plicker A wheel with an angular inertia of 56 kg-m 2 rotates at 55 rpm. What constant torque is required to stop the wheel in 15 seconds? a) b) c) d) 930 N-m 160 N-m 22 N-M 1300 N-m

Circular Motion and Rotation 02/25/20 Write in Notebook Rolling Kinetic Energy, Rotation and Translation

Circular Motion and Rotation 02/25/20 Write in Notebook Rolling Kinetic Energy, Rotation and Translation • We have seen that the kinetic energy of a wheel rolling on the ground is make of translational and rotational kinetic energy: 2 KE = ½ mv 2 + ½ I�� • Now let’s look at all the forces involved. • A wheel rolling with its own momentum has no friction at the point where the wheel contacts the ground.

Circular Motion and Rotation 02/25/20 Write in Notebook Friction and Rolling • However, if

Circular Motion and Rotation 02/25/20 Write in Notebook Friction and Rolling • However, if a force acts on the wheel, then it can slow down or speed up. • This acceleration will be both translational (a) and rotational (�� ). • If the contact point does not slide, then there will be a static frictional force there and the two accelerations are smooth and must follow: a = �� r • If on the other hand, the contact point slips, then there will be a kinetic frictional force there and the two accelerations are not related. �� f

Circular Motion and Rotation 02/25/20 Write in Notebook Acceleration Down a Ramp (No Slip)

Circular Motion and Rotation 02/25/20 Write in Notebook Acceleration Down a Ramp (No Slip) and Free Body Diagram • Applying Newton’s 2 nd Law along the x-axis to this situation gives: Fnet = fs - Fg sinθ = fs – Mg sinθ = M ax • At this point, we must realize that fs is not necessarily fs, max. • Now, applying Newton’s 2 nd Law to the rotation. FN τnet = Rfs = I �� xis R a x • Fn and Fg have no contribution to τnet , no moment arm. fs Fg sinθ • This torque is positive because it will rotate ccw. Fg cosθ • However, ax will be negative: �� = - ax/R Fg θ

Circular Motion and Rotation 02/25/20 Write in Notebook FN fs Fg sinθ This equation

Circular Motion and Rotation 02/25/20 Write in Notebook FN fs Fg sinθ This equation can be used with any round object Rolling down a ramp with I. Fg θ R xi x-a Fg cosθ s

Circular Motion and Rotation 02/25/20 Write in Notebook FN fs Fg sinθ In each

Circular Motion and Rotation 02/25/20 Write in Notebook FN fs Fg sinθ In each case, do we need the mass and radius? Fg Θ=30° R xi x-a Fg cosθ s

Circular Motion and Rotation 02/25/20 Homework Halliday, Resnick, Walker • From Chapter 11: •

Circular Motion and Rotation 02/25/20 Homework Halliday, Resnick, Walker • From Chapter 11: • CP 2 • Question 3 • Problem 5 • Vocabulary: • none Home Work Sheet Name Period Date Assigned Problems. Complete sentences Show math, units, sig. figs. Highlight or box answers 2. 5 m/s

Circular Motion and Rotation 02/26/20 Starter/Plicker In the situation pictured, a new force, FA,

Circular Motion and Rotation 02/26/20 Starter/Plicker In the situation pictured, a new force, FA, has been added to the rotational axis parallel to the ramp that prevents the wheel from moving. What is the static frictional force fs? a) b) c) d) 0. 00 N 2. 10 N 4. 20 N 8. 40 N FN Fg sinθ Fg Θ=30° R FA fs xi x-a Fg cosθ s

Circular Motion and Rotation 02/26/20 Write in Notebook T R θ Ro x Fg

Circular Motion and Rotation 02/26/20 Write in Notebook T R θ Ro x Fg

Circular Motion and Rotation 02/26/20 Write in Notebook Torque Cross Product • We have

Circular Motion and Rotation 02/26/20 Write in Notebook Torque Cross Product • We have defined torque for circular motion as the product of a perpendicular force acting at the radius. • Now, we will use a more general definition that applies to any particle moving in any direction with respect to an origin, O. • All these quantities are vectors and are related by the cross product: τ = r x F τ = r F sin θ F • The right hand rule gives the perpendicular direction. • Sweep fingers from r to F, when they are tail to tail. r

Circular Motion and Rotation 02/26/20 Write in Notebook Torque Cross Product τ = r

Circular Motion and Rotation 02/26/20 Write in Notebook Torque Cross Product τ = r x F = r F sin θ • Sample Problem 11 -3 F 1 = F 2 = F 3 = 2. 0 N r = 3. 0 m at θ = 30° in x-z plane F 3 What is the magnitude and direction of the Torque wrt the origin from each force? z F 1 r F 2 x θ y

Circular Motion and Rotation 02/26/20 Homework Halliday, Resnick, Walker • From Chapter 11: •

Circular Motion and Rotation 02/26/20 Homework Halliday, Resnick, Walker • From Chapter 11: • CP 3 • Question 5 • Problem 15, 19 • Vocabulary: • Cross product Home Work Sheet Name Period Date Assigned Problems. Complete sentences Show math, units, sig. figs. Highlight or box answers 2. 5 m/s

Circular Motion and Rotation 02/27/20 Substitute Lesson Plan Work on Homework Home Work Sheet

Circular Motion and Rotation 02/27/20 Substitute Lesson Plan Work on Homework Home Work Sheet Name Period Date Assigned Problems. Complete sentences Show math, units, sig. figs. Highlight or box answers 2. 5 m/s

Circular Motion and Rotation 02/28/20 Starter/Plicker What is the torque in unit vector notation

Circular Motion and Rotation 02/28/20 Starter/Plicker What is the torque in unit vector notation for the situation pictured? a) b) c) d) τ = 0. 0 i + 0. 0 j - 15 k (N-m) τ = 0. 0 i + 0. 0 j + 25 k (N-m) τ = 20 i + 0. 0 j + 0. 0 k (N-m) τ = 0 i + 15 j + 0. 0 k (N-m) y F=5 i+0 j (N) r=-4 i+3 j (m) x

Circular Motion and Rotation 02/28/20 Write in Notebook Angular Momentum • Recall that linear

Circular Motion and Rotation 02/28/20 Write in Notebook Angular Momentum • Recall that linear momentum is a powerful tool, because the momentum is conserved when there are no outside forces. • The same is true for angular momentum, which is the cross product of radius from an axis of rotation and the linear momentum: l = r x p = m (r x v) • If θ is the angle between r and p, then: l = mrv sin θ • The right hand rule gives the perpendicular direction. • Sweep fingers from r to p, when they are tail to tail. l = r x p p r

Circular Motion and Rotation 02/28/20 Write in Notebook Angular Momentum • Sample Problem 11

Circular Motion and Rotation 02/28/20 Write in Notebook Angular Momentum • Sample Problem 11 -4 l = mrv sin θ p 2 Two particle system. p 1=5. 0 kg m/s, r 1 will pass 2. 0 m at closest approach, ccw p 2=2. 0 kg m/s, r 2 will pass 4. 0 m at closest approach, cw l = l 1 - l 2 (right hand rule) l = p 1 r� 1 - p 2 r� 2 = 5. 0 • 2. 0 - 2. 0 • 4. 0 = 2. 0 m 2/s in (+z) p 1 r� 2 r� 1 O r 1

Circular Motion and Rotation 02/28/20 Write in Notebook Newtons 2 nd Law in Angular

Circular Motion and Rotation 02/28/20 Write in Notebook Newtons 2 nd Law in Angular Momentum • Recall that we can express Newton’s 2 nd Law in linear momentum: Fnet = ma = mdv/dt = dp/dt • Using angular motion terms: τnet = dl /dt

Circular Motion and Rotation 02/28/20 Write in Notebook Newtons 2 nd Law in Angular

Circular Motion and Rotation 02/28/20 Write in Notebook Newtons 2 nd Law in Angular Momentum Sample Problem 11 -5 Penguin falls from point A to a point at radius r with respect to the origin O. a) What is the angular momentum wrt O? • l = mv r� = m gt D (-z) b) What is the torque of the penguin about O? • τ = F D = mg D • or • τ = dl /dt = d(m gt D)/dt = mg. D “constant” y O D Ax

Circular Motion and Rotation 02/28/20 Homework Halliday, Resnick, Walker • From Chapter 11: •

Circular Motion and Rotation 02/28/20 Homework Halliday, Resnick, Walker • From Chapter 11: • CP 5 • Question 7 • Problem 27 • Vocabulary: • Angular Momentum Home Work Sheet Name Period Date Assigned Problems. Complete sentences Show math, units, sig. figs. Highlight or box answers 2. 5 m/s

Circular Motion and Rotation 03/2/20 Starter/Plicker What is the torque in unit vector notation

Circular Motion and Rotation 03/2/20 Starter/Plicker What is the torque in unit vector notation for the situation pictured? a) b) c) d) τ = 0. 0 i + 0. 0 j - 26 k (N-m) τ = 0. 0 i + 0. 0 j - 23 k (N-m) τ = 0. 0 i + 0. 0 j + 26 k (N-m) τ = 0. 0 i + 0. 0 j + 23 k (N-m) F=5 i+2 j (N) r=-4 i+3 j (m) y x

Circular Motion and Rotation 03/2/20 Write in Notebook

Circular Motion and Rotation 03/2/20 Write in Notebook

Circular Motion and Rotation 03/2/20 Write in Notebook

Circular Motion and Rotation 03/2/20 Write in Notebook

Circular Motion and Rotation 03/2/20 Write in Notebook Angular Momentum and a Rigid System

Circular Motion and Rotation 03/2/20 Write in Notebook Angular Momentum and a Rigid System of Particles • Our previous discussion holds for systems of particles rigidly tied together or not. • If we narrow our consideration to systems of particles that are held together rigidly and consider the rotation about the z-axis then: • We dropped the z reference because I is simply about the rotational axis, which happened to be z.

Circular Motion and Rotation 03/2/20 Write in Notebook More Rotational to Translational Relationships Pure

Circular Motion and Rotation 03/2/20 Write in Notebook More Rotational to Translational Relationships Pure Translation (Fixed Direction) Force F=ma Linear Momentum p P = �� pi Linear Momentum b Newton’s 2 nd Law b Conservation Law d P = M vcom Fnet= d. P/dt P = constant b: for systems of particles rigid or not c: for rigid objects about a fixed axis, L along that axis d: For a closed isolated system, no external forces. Pure Rotation (Fixed Axis) Torque τ = r x F τ = I �� Torque A. Momentum b A. Momentum c Newton’s 2 nd Law b Conservation Law d L = I �� τ net= d. L/dt L = constant

Circular Motion and Rotation 03/2/20 Homework Halliday, Resnick, Walker • From Chapter 11: •

Circular Motion and Rotation 03/2/20 Homework Halliday, Resnick, Walker • From Chapter 11: • CP 6 • Problem 35 • Vocabulary: • None Home Work Sheet Name Period Date Assigned Problems. Complete sentences Show math, units, sig. figs. Highlight or box answers 2. 5 m/s

Circular Motion and Rotation 03/3/20 Starter/Plicker p=-5 i+2 j (kg m/s) y r=-4 i+3

Circular Motion and Rotation 03/3/20 Starter/Plicker p=-5 i+2 j (kg m/s) y r=-4 i+3 j (m) x

Circular Motion and Rotation 03/3/20 Write in Notebook Conservation of Angular Momentum • A

Circular Motion and Rotation 03/3/20 Write in Notebook Conservation of Angular Momentum • A powerful tool was the conservation of linear momentum. Pi = Pf (isolated system) • The same is true for the conservation of angular momentum. Li = Lf (isolated system) Ii �� i= If �� f (isolated system) • Like conservation of linear momentum, conservation of angular momentum in the special relativity and quantum reigns

Circular Motion and Rotation 03/3/20 Write in Notebook Conservation of Angular Momentum • Sample

Circular Motion and Rotation 03/3/20 Write in Notebook Conservation of Angular Momentum • Sample Problem 11 -7 Iwh = 1. 2 kg m 2, �� 1=3. 9 rev/s ccw I 2 = 6. 8 kg m 2 (boy and wheel) What is final �� 2 f when wheel if flipped over? • Sample Problem 11 -8

Circular Motion and Rotation 03/3/20 Homework Halliday, Resnick, Walker • From Chapter 11: •

Circular Motion and Rotation 03/3/20 Homework Halliday, Resnick, Walker • From Chapter 11: • CP 7 • Problem 43 • Vocabulary: • None Home Work Sheet Name Period Date Assigned Problems. Complete sentences Show math, units, sig. figs. Highlight or box answers 2. 5 m/s

Circular Motion and Rotation 03/4/20 Starter/Plicker

Circular Motion and Rotation 03/4/20 Starter/Plicker

Circular Motion and Rotation 03/4/20 Write in Notebook Gyroscope • If a non-spinning gyroscope

Circular Motion and Rotation 03/4/20 Write in Notebook Gyroscope • If a non-spinning gyroscope is placed on its support with the shaft 90° to the support, it will fall. τ = R x Fg = R x mg = d. L/dt • When not spinning, τ is into the screen and the gyroscope rotates downward about its pivot. com R Fg

Circular Motion and Rotation 03/4/20 Write in Notebook Gyroscope • If the gyroscope is

Circular Motion and Rotation 03/4/20 Write in Notebook Gyroscope • If the gyroscope is spinning, it will not fall, but instead will precess. τ = R x Fg = R x mg = d. L/dt • In stead of starting from zero, the initial L is that of the spinning gyroscope, L= I�� • In addition, d. L = τ dt, which is still into the screen. • After time dt, L(dt)=L(0) + d. L L(dt) • The magnitude of L stays the same, but changes L direction from the z-axis. • The precession is clockwise as shown in the diagram with the precession circle perpendicular to the screen about the z-axis. z com R Fg

Circular Motion and Rotation 03/4/20 Write in Notebook com d. L dφ R L

Circular Motion and Rotation 03/4/20 Write in Notebook com d. L dφ R L Fg

Circular Motion and Rotation 03/4/20 Homework Halliday, Resnick, Walker • From Chapter 11: •

Circular Motion and Rotation 03/4/20 Homework Halliday, Resnick, Walker • From Chapter 11: • Problem 47, 61 • Vocabulary: • Precession Home Work Sheet Name Period Date Assigned Problems. Complete sentences Show math, units, sig. figs. Highlight or box answers 2. 5 m/s

Circular Motion and Rotation 03/5/20 Starter/Plicker

Circular Motion and Rotation 03/5/20 Starter/Plicker

Circular Motion and Rotation 03/5/20 Write in Notebook Additional Problems Practice • Problem 11

Circular Motion and Rotation 03/5/20 Write in Notebook Additional Problems Practice • Problem 11 -77 Girl Mass=M, Merry-Go-Round R and I, originally at rest. Rock mass=m, v • Problem 11 -79 y rxp = rxpy - pxry p = -2. 4 sin(25 °) i + 2. 4 cos(25 °)j (m/s) y p 25° r x r = 2. 0 i + 3. 0 j (m) 115° x

Circular Motion and Rotation 03/5/20 Homework Halliday, Resnick, Walker • From Chapter 11: •

Circular Motion and Rotation 03/5/20 Homework Halliday, Resnick, Walker • From Chapter 11: • Problem 83, 87 • Vocabulary: • None Home Work Sheet Name Period Date Assigned Problems. Complete sentences Show math, units, sig. figs. Highlight or box answers 2. 5 m/s

Circular Motion and Rotation 03/9/20 Starter/Plicker

Circular Motion and Rotation 03/9/20 Starter/Plicker

Circular Motion and Rotation 03/9/20 Write in Notebook I=½ MR 2 M=10 kg R=0.

Circular Motion and Rotation 03/9/20 Write in Notebook I=½ MR 2 M=10 kg R=0. 1 m T R θ Ro Fg Fapp=12 N F s

Circular Motion and Rotation 03/9/20 Homework Halliday, Resnick, Walker • From Chapter 11: •

Circular Motion and Rotation 03/9/20 Homework Halliday, Resnick, Walker • From Chapter 11: • Problem 95 • Vocabulary: • None Home Work Sheet Name Period Date Assigned Problems. Complete sentences Show math, units, sig. figs. Highlight or box answers 2. 5 m/s

Circular Motion and Rotation 03/10/20 Starter/Plicker The tire pictured rotates clockwise and its axle

Circular Motion and Rotation 03/10/20 Starter/Plicker The tire pictured rotates clockwise and its axle is tied to a rope in the back. Which direction does it precess? a) b) c) d) CW Looking down from top CCW looking down from the top Downward Upward

Circular Motion and Rotation 03/10/20 Write in Notebook Equilibrium Force and Torque • An

Circular Motion and Rotation 03/10/20 Write in Notebook Equilibrium Force and Torque • An object will topple if its cog is beyond its furthest point of support.

Circular Motion and Rotation 03/10/20 Write in Notebook y 6. 0 m 15 kg

Circular Motion and Rotation 03/10/20 Write in Notebook y 6. 0 m 15 kg 25 kg x 4. 0 m 6. 0 m 8. 0 m

Circular Motion and Rotation 03/10/20 Write in Notebook Equilibrium Force and Torque • Newton’s

Circular Motion and Rotation 03/10/20 Write in Notebook Equilibrium Force and Torque • Newton’s 2 nd Law in the forms of linear and angular momentum: Fnet = d. P/dt and τnet = d. L/dt • If the net force and torque are zero, this tells us that an object is in dynamic equilibrium. The vector sums of all the external forces and torques are zero. • To be in static equilibrium, the linear momentum must also be zero. P=0

Circular Motion and Rotation 03/10/20 Write in Notebook Equilibrium Force and Torque • We

Circular Motion and Rotation 03/10/20 Write in Notebook Equilibrium Force and Torque • We can examine F and τnet by examining each of their x, y, z components separately. Balance of Forces Fnet , x = 0 Fnet , y = 0 Fnet , z = 0 Balance of Torques τnet, x = 0 τnet, y = 0 τnet, z = 0 • We will examine situations in the x-y plane, so the set of the above equations is then limited to: Fnet , x = 0 Fnet , y = 0 τnet, z = 0 • Recall that if forces are limited to the x-y plane then torques is limited to directions parallel to the z-axis.

Circular Motion and Rotation 03/10/20 Write in Notebook Equilibrium Force and Torque • The

Circular Motion and Rotation 03/10/20 Write in Notebook Equilibrium Force and Torque • The last thing we need to know to examine equilibrium situations is: • The gravitational force on a rigid body acts on a single point, called the center of gravity. • If gravity is the same for all elements of the body, then the body’s cog is the same as the com. • Seems obvious. But very tall buildings have less gravity at the top than at the bottom. Therefore, the center of gravity can be lower than the center of mass by about 1 mm.

Circular Motion and Rotation 03/10/20 Homework Halliday, Resnick, Walker From Chapter 12: • Check

Circular Motion and Rotation 03/10/20 Homework Halliday, Resnick, Walker From Chapter 12: • Check Point 1 • Question 1 • Problem 2 Vocabulary: • Dynamic Equilibrium, Static Equilibrium Topple Home Work Sheet Name Period Date Assigned Problems. Complete sentences Show math, units, sig. figs. Highlight or box answers 2. 5 m/s

Circular Motion and Rotation 03/11/20 Starter/Plicker y Will it topple? a) b) c) d)

Circular Motion and Rotation 03/11/20 Starter/Plicker y Will it topple? a) b) c) d) 6. 0 m Will topple to the right Will topple to the left Will topple upward Will not topple 15 kg 25 kg x 4. 0 m 6. 0 m 8. 0 m

y Circular Motion and Rotation 03/11/20 F 1 F 2 Write in Notebook o

y Circular Motion and Rotation 03/11/20 F 1 F 2 Write in Notebook o L L/4 x z mg Mg Fw y a/2 h a/3 F py Mg mg o fpx moment arms x

Circular Motion and Rotation 03/11/20 y Write in Notebook b=2. 5 m Tc a=1.

Circular Motion and Rotation 03/11/20 y Write in Notebook b=2. 5 m Tc a=1. 9 m Fv mg x Fh Mg

Circular Motion and Rotation 03/11/20 Homework Halliday, Resnick, Walker • From Chapter 12: •

Circular Motion and Rotation 03/11/20 Homework Halliday, Resnick, Walker • From Chapter 12: • Check Point 4 • Question 3 • Problem 5, 9, 13 • Vocabulary: • none Home Work Sheet Name Period Date Assigned Problems. Complete sentences Show math, units, sig. figs. Highlight or box answers 2. 5 m/s

y Circular Motion and Rotation 03/12/20 Starter/Plicker For the diagram at the right, the

y Circular Motion and Rotation 03/12/20 Starter/Plicker For the diagram at the right, the green cable will break at 1200 N. The blue beam has a mass of 500 N and is 3. 00 m. To prevent the cable from breaking, but have as high a tension on the cable as possible, which is most true? a) b) c) d) H>0. 625 m H<0. 625 m H>1. 25 m H<1. 25 m H Tc L=3. 00 m M=500 N x

Circular Motion and Rotation 03/12/20 Halliday, Resnick, Walker • Work Problems on the Board

Circular Motion and Rotation 03/12/20 Halliday, Resnick, Walker • Work Problems on the Board • Ask for volunteers. • From Chapter 12: • Check Point 4 • Question 3 • Problem 5, 9, 13 • We are working on problems using three equations one torque and two force balances. Therefore, we can solve for three unknowns. If the problem has four unknowns, it is indeterminate.

Circular Motion and Rotation 03/12/20 Homework Halliday, Resnick, Walker • From Chapter 12: •

Circular Motion and Rotation 03/12/20 Homework Halliday, Resnick, Walker • From Chapter 12: • Problem 25, 27 • Vocabulary: • Indeterminate Home Work Sheet Name Period Date Assigned Problems. Complete sentences Show math, units, sig. figs. Highlight or box answers 2. 5 m/s

Circular Motion and Rotation 03/13/20 Starter/Plicker For the diagram at the right, what force

Circular Motion and Rotation 03/13/20 Starter/Plicker For the diagram at the right, what force does B apply to the board. Both A and B are fixed to the board that supports mass M=580 N. The length to the mass is 3. 00 m from B and A is 1. 50 m from B. The board is massless. a) b) c) d) 1160 upward 1160 downward 1740 upward 1740 downward M=580 N L=3. 0 m l=1. 5 m A x B

Circular Motion and Rotation 03/13/20 Write in Notebook Elasticity • We have looked at

Circular Motion and Rotation 03/13/20 Write in Notebook Elasticity • We have looked at materials as rigid. Real materials are elastic. • When we apply a force (stress) to an object, we deform (strain) the object. • Tensile stress is associated with stretching. • Sheering stress is associated with side to side forces. • Hydraulic stress is associated with forces from all directions.

Thermal Energy 03/13/20 Write in Notebook Solids • Most materials respond in a similar

Thermal Energy 03/13/20 Write in Notebook Solids • Most materials respond in a similar manner when stained. • When stress is limited to the yield point, materials return to their original shape, elastic. • After that, the stress results in permanent shape change, plastic. • After the plastic region, the additional stress breaks the object.

Circular Motion and Rotation 03/13/20 Write in Notebook Elasticity • In the elastic region

Circular Motion and Rotation 03/13/20 Write in Notebook Elasticity • In the elastic region of a stress vs. strain curve, the stress is related to the strain by the modulus: stress = modulus x strain • If the stress goes beyond the yield strength, the object is permanently damaged. It does not recover its shape. • If the stress continues to the ultimate strength, the object breaks.

Circular Motion and Rotation 03/13/20 Write in Notebook

Circular Motion and Rotation 03/13/20 Write in Notebook

Circular Motion and Rotation 03/13/20 Homework Halliday, Resnick, Walker • From Chapter 12: •

Circular Motion and Rotation 03/13/20 Homework Halliday, Resnick, Walker • From Chapter 12: • Check Point 6 • Question 9 • Problem 63 • Vocabulary: • Stress, strain, modulus, yield strength, ultimate strength Home Work Sheet Name Period Date Assigned Problems. Complete sentences Show math, units, sig. figs. Highlight or box answers 2. 5 m/s

Circular Motion and Rotation 03/16 -17/20 2 -day Lab Static Torque 1. Build the

Circular Motion and Rotation 03/16 -17/20 2 -day Lab Static Torque 1. Build the support structures pictured on the back (x 3). 2. Measure the mass of the beam and weight using an electronic balance. 3. Measure the tension on the string by incorporating a scale. 4. Measure the appropriate angles or distances. 5. Using the measured masses, calculate the tension on the string. 6. Compare measure to calculated tensions. (Write this in Report) Names Date Period Lab Report Name of Lab Scientific Question: How can one use static torque to predict string tensional forces? Diagram: Diagram three structures and label all angles, forces and torques. Procedure: So someone else could follow. Include drawings of structures. Refer to diagram. Data: Organized in a Table with units and sig. fig Calculations: Show all calculation to determine tension. Results: List measured and calculated values with units and sig. fig. Discussion: Talk about the test. Compare measurements. Discuss error and likely source. Suggest improvements.

Circular Motion and Rotation 03/18 -19/20 2 -day Lab Static Torque 1. Build the

Circular Motion and Rotation 03/18 -19/20 2 -day Lab Static Torque 1. Build the support structures pictured on the back (x 3). 2. Measure the mass of the beam and weight using an electronic balance. 3. Measure the tension on the string by incorporating a scale. 4. Measure the appropriate angles or distances. 5. Using the measured masses, calculate the tension on the string. 6. Compare measure to calculated tensions. (Write this in Report) Names Date Period Lab Report Name of Lab Scientific Question: How can one use static torque to predict string tensional forces? Diagram: Diagram three structures and label all angles, forces and torques. Procedure: So someone else could follow. Include drawings of structures. Refer to diagram. Data: Organized in a Table with units and sig. fig Calculations: Show all calculation to determine tension. Results: List measured and calculated values with units and sig. fig. Discussion: Talk about the test. Compare measurements. Discuss error and likely source. Suggest improvements.

Circular Motion and Rotation 03/23/20 Starter/Plicker A 2. 0 kg mass hangs from massless

Circular Motion and Rotation 03/23/20 Starter/Plicker A 2. 0 kg mass hangs from massless cables. What is the tension on cable B, TB? Where the mass hangs, cable B is 60 ° from horizontal and cable A is 20° from horizontal. a) b) c) d) 15 N 28 N 36 N 57 N TB θ 1 = 60° θ 1 = 20° TA M=2. 0 kg

Circular Motion and Rotation 03/23/20 θ Write in Notebook T c a 60° φ1

Circular Motion and Rotation 03/23/20 θ Write in Notebook T c a 60° φ1 φ2 b mg

Circular Motion and Rotation 03/23/20 Write in Notebook Problems Involving Static Equilibrium Problem 12

Circular Motion and Rotation 03/23/20 Write in Notebook Problems Involving Static Equilibrium Problem 12 -67: Beam mass =m. 60° from wall. What is Tension on cable, T? Wat is Force on hinge in unit vector notation? τnet= 0 = 2. 0 Tcos 25 – 3. 2 Ft (Bal. of torques) Fx, net= 0 = Fx –T cos 25 + Ft (Bal. of Forces) Fy, net= 0 = Fy-T sin 25 - Fg Ft=50 N Fg=60 N H=3. 2 m T 25° Fy h=2. 0 m Fx

Circular Motion and Rotation 03/23/20 Write in Notebook 250 kg 46 kg Problems Involving

Circular Motion and Rotation 03/23/20 Write in Notebook 250 kg 46 kg Problems Involving Static Equilibrium F 2 F 1 5. 0 m Problem 12 -73: Beam=250 kg. Gymnast=46 kg at end of beam. Each is 0. 54 m from post. 0. 54 mo 1. 96 m 0. 54 m What is force on each post? Fg τnet= 0 = F 10 -250 x 9. 8 x 1. 96+F 2 x 3. 92 -46 x 9. 8 x 4. 46 Fy, net= 0 = F 1 + F 2 – 250 x 9. 8 – 46 x 9. 8

Circular Motion and Rotation 03/23/20 Write in Notebook Ft frictionless θ θ 200 N

Circular Motion and Rotation 03/23/20 Write in Notebook Ft frictionless θ θ 200 N 10 m F=50 N or 150 N Fby d θ Fbx 8 m

Circular Motion and Rotation 03/23/20 Homework Halliday, Resnick, Walker • From Chapter 12: •

Circular Motion and Rotation 03/23/20 Homework Halliday, Resnick, Walker • From Chapter 12: • Problem 47, 53, 55 • Vocabulary: • none Home Work Sheet Name Period Date Assigned Problems. Complete sentences Show math, units, sig. figs. Highlight or box answers 2. 5 m/s

Circular Motion and Rotation 03/24/20 Starter/Plicker The leaning tower of Pisa is 55 m

Circular Motion and Rotation 03/24/20 Starter/Plicker The leaning tower of Pisa is 55 m high an has a 7. 0 m base. It is currently 4. 5 m displaced at the top. Treating it as a cylinder, at what angle would the tower to topple? a) b) c) d) 2. 3° 4. 7° 6. 3° 7. 3° 4. 5 m 55 m

Circular Motion and Rotation 03/24/20 • • • CRAM Sheet Unit 5 Tuesday CRAM

Circular Motion and Rotation 03/24/20 • • • CRAM Sheet Unit 5 Tuesday CRAM Sheet (3/24/20) Wednesday CRAM Sheet (3/25/20) Thursday CRAM Sheet (3/26/20) Friday Unit 5 Test (3/27/20) Unit 6 Starting (3/30/20)