It doesnt seem stable why doesnt it fall

It doesn’t seem stable why doesn’t it fall? Center of Mass Balanced Rock Arches National Park Moab, Utah

When a ball is spun in the air it spins around its center & so does a block of wood That is to say the axis of rotation is through the center of the object A hammer behaves a little differently

An object naturally spins around its: center of mass which is very similar to (we will use these interchangeably) center of gravity

Center of Gravity or Center of Mass This is a location of the average position of mass in an object CM

If an object is symmetrical and uniform (made of the same material throughout) the center of mass is just the center CM

If an object has more mass at one end, the center of mass if shifted that way CM Lead Plastic

Where is the center of mass?

Where would the CM of a large pot be?

But you can’t just say that there is the same amount of mass to the left and to the right Where At what do point you think would this there set of be masses the same connected mass to bythe a string left & would right (assume rotate about the string if swung is massless) in the air Actual CM 1 kg Equal mass L/R & U/D 2 kg Geometric center shown at line

Multiply the mass times its distance from the center of mass Actual CM 1 kg 1 m 2 m * 1 kg 1 m 1 m 2 kg 1 m * 2 kg

A massive sun and 3 small planets. Where is the center of mass? Sun CM

The solar system does NOT rotate around the center of the sun. Sun

The sun actually wobbles a bit because… Sun

Does the center of mass of our solar system change or is it constant? Sun

Compare the center of mass after the explosion? If there are no outside forces, the center of mass is the same based on conservation of momentum

What if the fragments are different sizes?

Why does a washing machine vibrate during the spin cycle sometimes but not others? Where is the center of mass

If a puck is pushed across a frictionless table It moves in a straight line at a constant speed

A motion graph for this is…

If a wrench is slid across a frictionless table The wrench below spins about is CM And its CM moves in a straight line at a constant speed

If a baseball is thrown into the air it follows a parabolic path

If a bat is tossed it looks a little more chaotic but….

But really just 2 things happen 1. ) the object rotates around its CM 2. ) the CM follows a parabolic path

Complex motion like the hammer can be simplified 1. ) The CM moves (translates) in a straight line or parabola 2. ) The object rotates around the CM APPLET

If ball is thrown into the air, it follows a parabolic path (sorry can’t control the speed any better)

The hammer does 2 things when tossed 1. ) rotates around the CM 2. ) the CM follows the typical path

Now at the same time.

A hammer thrown into the air

The center of mass / center of gravity is special for several reasons.

FOR EXAMPLE: Gravity pulls down on an entire meter stick (each atom) Fg BUT this would make calculations a bit tiresome

FOR EXAMPLE: Fg = mg BUT you can PRETEND like the Force of gravity is only pulling down on the CENTER OF MASS

FN = mg Fg = mg When a fulcrum is placed under the CM, It balances!!! (the net force is zero)

This is an easy way to find the center of mass of an object JUST BALANCE IT ON YOUR FINGER

If a weight is hung at one end, what happens to the CM

A Force causes acceleration A Torque causes angular acceleration (rotation) Force Torque

Anytime you rotate an object you apply a torque

When you open door, it rotates. Where is the pivot point / axis of rotation?

To open a heavy door where would you push on the door to make it easiest? A B C

The distance from the pivot point to the location of the force is called the LEVER ARM (distance) A B C The longer the lever arm the greater the torque

This force has no lever arm and produces no torque or rotation

The direction of the force matters too, how well will these two forces work for opening the door? B A

To Rotate an object the force must be applied perpendicular to the lever arm (the door in this case) B A A is perpendicular to the lever

TORQUE t=Fd Force perpendicular to lever arm (N) lever arm length (m) NOT distance traveled

Where should you push the wrench in order to loosen a stubborn bolt? t=Fd Torque Force MORE Torque Force

A wrench is all about TORQUE You create the most torque by holding the wrench at the end and by exerting a large force. If you can’t loosen the bolt with all your strength, what do you do?

Force Get a longer wrench!! lever arm Even with the same force, twice the lever arm gives twice the TORQUE

The greater the force, the greater the torque t=Fd Torque Force MORE Torque

The more perpendicular the force the greater the torque t=Fd Torque Force only the blue part counts MORE Torque Force

Any force which points through the axis of rotation creates no torque Force t=Fd Torque = 0

Torque requirement on your tires lug nuts is 190 Nm. If you have a wrench which is. 25 m, how hard do you have to push? . 25 m

A force of 70 N is exerted as below on a. 25 m wrench. What torque is generated? 70 N. 25 m 35 o

Consider the two wrenches below, compare torques If the applied force is the same F F

The lever arm distance is really still the same F F

Another way of looking at torque, this is easier in some situtations. 1. ) Draw a line through the force 2. ) Bring a line perpendicular to the previous line through the axis of rotation 3. ) The lever arm is the distance that line to the center of rotation lever arm distance 4. ) Torque = Total force x lever arm

1. ) Draw a line through the force 2. ) The lever arm is the distance that line to the center of rotation 3. ) Torque = Total force x lever arm Lever arm distance (d) F

1. ) Draw a line through the force 2. ) The lever arm is the distance that line to the center of rotation 3. ) Torque = Total force x lever arm F Lever arm distance (d)

A force of 100 N is exerted as below on a rope attached to a. 25 m wrench. What torque is generated? 100 N . 2 m

F

Using the 2 nd method to find the torque A force of 70 N is exerted as below on a. 25 m wrench. What torque is generated? 70 N . 25 m 35 o

Torque Feeler DEMO

TORQUE is also a vector. There are two ways of looking at finding the direction of torque. 1. ) Look at the angular velocity the torque would give the object. Use the right hand rule

Where does the torque vector point? F

A mass on a string exerts a torque on a pulley, what is the direction of the torque vector?

20. 0 N 4. 0 m from fulcrum 30 N 2. 0 m from fulcrum What is the net torque on the see saw (ignoring the mass of the seesaw itself)?

4. 0 m from fulcrum 20 N What is the net torque on the see saw (ignoring the mass of the seesaw itself)? 2. 0 m from fulcrum 30 N

What is the net torque on the wheel and axle below? . 25 m. 10 m 40 N 20 N

DEMONSTRATION: Will the object rotate . 10 m 500 g . 25 m 500 g

Does a thicker wrench give you more torque? Does a thicker screwdriver? TORQUE FEELER DEMO

Torque WS 1

What Force(s) are acting on a rolling ball? Is the force of gravity causing a torque? Fg

What else is acting on the ball FN Fg Will the normal force cause a torque?

What else is acting on the ball Friction is the only force causing a torque FF FN Fg

When a football spins in the air where is the axis of rotation? Through the center of mass!

When a force is applied through the CM. Will it accelerate? YES Will it rotate? Is there torque?

What about here-Will it accelerate? YES Will it rotate? rotate- Is there torque YES

Will it accelerate? YES Will it rotate?

Balanced Torques

Two 400 N children balance on a seesaw The same force on each side, right 400 N 1 m 1 m

What if one child scoots in? Forces are still equal on both sides 400 N 1 m 0. 5 m

All forces would cancel (adding the fulcrum) BUT THE TORQUES DO NOT 400 N 1 m t = 400 Nm (CCW) 0. 5 m t = 200 Nm (CW) Net t = 200 Nm (CCW)

If an object is balanced there can be NO NET TORQUE in other “words” Stcw = Stccw

Can a big kid and a little kid balance on a seesaw? 400 N 100 N

Can a big kid and a little kid balance on a seesaw? 400 N 100 N ? 1 m What would happen if the 100 N person leaned forward?

A 250 N child sits 1. 0 meter away from the pivot point. Where should a 325 N adult sit for the see saw to balance? 325 N ? 250 N 1. 0 m

How much force needs to be placed at the 9 m mark to balance the board? 9 ? N 8 7 6 5 100 N 4 3 2 1 0 500 N

A 150 kg beam which 8. 0 m long and is supported by a fulcrum 2. 5 m from one end. How much force must be applied to one of the ends to balance the object?

A 100 kg beam which 10. 0 m long and is supported by a rope 4. 0 m from one end. An additional force of 2, 000 N is applied 2 meters from the same end pulling down. Where should a 800 N downward force be place to cancel? 2, 000 N 800 N where to place

Torque problems Balanced Torque Lab

In order for an object to be perfectly still or static, 2 Conditions MUST BE MET #1 All FORCES must cancel #2 All TORQUES must cancel

Will this object accelerate or rotate? Consider the CM its center of rotation 100 N

Will this object accelerate or rotate? 100 N

Will this object accelerate or rotate? 100 N 200 N 100 N

Consider an object in space with only 2 forces on it. Will the object accelerate or rotate? 100 N

Will this object accelerate or rotate? 100 N 50 N

Will this object accelerate or rotate? 100 N 150 N

Statics- Getting things not to move If an object is completely stationary it is said to be static It must not ROTATE OR ACCELERATE Neither of these are good for a building!!!

Rotation and Acceleration is bad!! (although some flex is necessary)

Many factors need to be considered when designing a structure such as: Wind / Earthquake resistance Moving loads (like semi-trucks) Strength of materials But the first is just supporting its own weight and anticipated loads

TWO criteria must be met 1 st all forces cancel S FX =0 lefts = rights S FY =0 ups = downs

But just having the FORCES cancel, isn’t enough. Consider the bridge below, a 5, 000 N car on top of a 90, 000 N bridge is supported by 1 column. Forces balance. But UH OH 95, 000 N 90, 000 N

TWO criteria must be met 2 nd all Torques cancel S t =0 or tcw = tccw

In order for the paint stick to be “static” Forces and Torques must cancel

In order for the paint stick to be “static” Forces and Torques must cancel A B D C A+B+C+D=0 C & D are negative

In order for the paint stick to be “static” Forces and Torques must cancel d. A A B D C d. D d. C Still keeping C & D negative Ad. A + Cd. C + Dd. D = 0

A massless meter stick is supported by 2 spring scales. A 1. 0 kg mass is hung at the 25 cm mark. What is the force exerted by each scale if the meterstick is static?

1 st - sum of all forces = 0 UPS = DOWNS FA A FB 25 cm C 100 cm 9. 8 N FA + FB = 9. 8 N B

2 nd - sum of all torques = 0 What should be do about center of rotation for lever arm Should we use A, B, C, or D? FA A FB 25 cm C 9. 8 N D B

TRICK #1 You can use ANY POINT as the center of rotation. Because a static object will not rotate about ANY POINT. BUT BE CONSISTENT!!!!!!!!! Pick a convenient location- such as one with a unkown force on it. This way it has no lever arm and therefore no torque. This simplifies your equation.

2 nd - sum of all torques = 0 CW = CCW Lets use point A. FA FB B C A 9. 8 N t. C = t. B 9. 8 N. 25 m = 1. 0 m FB

DO the same thing using point C UPS = DOWNS & LEFTS = RIGHTS CW = CCW FA FB 25 cm C A 9. 8 N 100 cm B

A 65 kg person stands on a 6. 0 m long plank (ignore it weight). Where should they stand so that the tension in the left cable is 180 N.

A 25 kg cantilevered pole is supported by 2 posts. Find the force exerted by each on the pole. 5 m A B 8 m C 16 m D

TRICK #2 You may not know the direction of a force. Just pick a direction. If you answer ends up negative, it just means it goes opposite the way you have drawn.

5 m A FA B FB 7 m C 14 m D Fg = 25 kg * 9. 8 m/s 2

5 m A FA B FB 7 m C Fg = 245 N 15 m D

a 7 kg beam 3 m long is held by a hinge and cable. What are the forces at pts A & B. The tension in the cable? 36 o A 3. 0 m B

a 7 kg beam supporting a 11 kg mass 36 o A B. 5 m 2. 5 m 11 kg

A 5 m ladder with a mass of 12 kg is supported at the floor and frictionless wall. What are the forces on the ladder? 5 m 4 m 3 m

Problems: Honors Physics p 267 -268 handout prob optional 19, 23, 25, 26 542 N, 409 N, -59 N A 25 kg board (8 m long) leans against a wall. Indicate all forces involved. 60 o (245, 71)