Circular Motion ChinSung Lin Rotation Revolution Axis Rotation
- Slides: 68
+ Circular Motion Chin-Sung Lin
+ Rotation & Revolution Axis Rotation Revolution
+ Period & Frequency Period (T): seconds/cycle Radius (r) Frequency (f): cycles/second (Hz)
+ Period & Frequency Radius (r) T = 1/f f = 1/T
+ Period & Frequency Exercise Radius (r) If the frequency is 40 Hz, what’s the period?
+ Period & Frequency Exercise Radius (r) If the period is 0. 05 s, what’s the frequency?
+ Period & Frequency If the microprocessor clock of your computer is running at 2. 5 GHz, what’s the period of the clock?
+ Rotational & Linear Speed r R A 2πr A A B 2πR B B
+ Rotational & Linear Speed r R A 2πr A A B 2πR B B ? ? ? 2πR = 2πr ? ? ?
+ Rotational & Linear Speed Linear speed: distance moved per unit of time r v = Δd / Δt The linear speed is greater on the outer edge of a rotational object than it is closer to the axis R
+ Rotational & Linear Speed Tangential speed: The speed of an object moving along a circular path can be called tangential speed because the direction of motion is always tangent to v the circle v v v
+ Rotational & Linear Speed For circular motion, tangential speed = linear speed
+ Rotational & Linear Speed Linear / Tangential Speed (v): Circumference = 2πr Period = T Radius (r) Linear/Tangential Speed = 2πr / T = 2πrf
+ Rotational & Linear Speed Exercise Linear / Tangential Speed (v): Period = 2 s Tangential Speed ? 3 m
+ Rotational & Linear Speed Exercise Linear / Tangential Speed (v): Frequency = 2 Hz Tangential Speed ? 4 m
+ Rotational & Linear Speed Exercise Linear / Tangential Speed (v): Frequency = ? Tangential Speed = 12π m/s Period = ? 2 m
+ Rotational & Linear Speed Rotational / Angular speed ( ): The number of rotations per unit of time All parts of a rotational object have the same rate of rotation, or same number of rotations per unit of time Unit of rotational speed: n Degrees/second or radians/second n Revolutions per minute (RPM)
+ Rotational & Linear Speed Rotational / Angular speed ( ): 1 revolution = 2π Period = T Radius (r) Rotational Speed �= 2π/T = 2πf (rads/s)
+ Rotational & Linear Speed Exercise Rotational / Angular speed ( ): Period = 2 s Rotational Speed = ? 5 m
+ Rotational & Linear Speed Exercise Rotational / Angular speed ( ): Frequency = 2 Hz Rotational Speed = ? 5 m
+ Rotational & Linear Speed Rotational / Angular speed ( ): Rotational Speed = 2πf (rads/s) Tangential Speed v = 2πrf (m/s) v = r (Tangential speed) = (Radial distance) x (Rotational speed)
+ Rotational & Linear Speed Rotational / Angular speed ( ): At the center (or axis) of the rotational platform, there is no tangential speed, but there is rotational speed
+ Rotational & Linear Speed Exercise Rotational / Angular speed ( ): Rotational Speed = 4π Linear Speed = ? 3 m
+ Rotational & Linear Speed Exercise Rotational / Angular speed ( ): Linear Speed = 6π m/s Rotational Speed = ? 2 m
+ Rotational & Linear Speed Exercise Rotational / Angular speed ( ): Period = 3 s 4 m 2 m Rotational Speed = ? B A Linear Speed = ?
+ Rotational & Linear Speed r R A B
+ Rotational & Linear Speed r R A 2πR A A B 2πR B B 2πR
+ Centripetal Force & Acceleration
+ Centripetal Force & Acceleration Centripetal Force Inertia
+ Centripetal Force & Acceleration
+ Centripetal Force & Acceleration
+ Centripetal Force & Acceleration Centripetal Force Inertia
+ Centripetal Force & Acceleration Centripetal Acceleration is a vector quantity a = Δv / Δt Velocity can be changed by increasing/ decreasing the magnitude of v, or changing the direction
+ Centripetal Force & Acceleration Centripetal Acceleration A A B D C C Change Speed D B Change Direction
+ Centripetal Force & Acceleration Centripetal Acceleration An object moves around in a circle with constant speed has acceleration, because its direction is constantly changing This acceleration is called centripetal acceleration (Ac)
+ Centripetal Force & Acceleration Centripetal acceleration is directed toward the center of the circle Ac Ac
+ Centripetal Force & Acceleration Centripetal Acceleration An acceleration that is directed at a right angle to the path of a moving object and produces circular motion Centripetal acceleration (Ac) Ac = 2 v /r
+ Centripetal Force & Acceleration Centripetal Acceleration Ac = v 2 / r = (r ) 2 / r = r 2 Ac = 2 v / r = r 2
+ Centripetal Acceleration Exercise Centripetal Acceleration (Ac): Linear speed = 6 m/s 3 m Centripetal Acceleration = ?
+ Centripetal Acceleration Exercise Centripetal Acceleration (Ac): Rotational speed = 2 rad/s 3 m Centripetal Acceleration = ?
+ Centripetal Acceleration Exercise Centripetal Acceleration (Ac): Period = 2 s Centripetal Acceleration = ? 5 m
+ Centripetal Force & Acceleration Centripetal Force Centripetal force is a force directed toward the center of the circle Fc Fc
+ Centripetal Force & Acceleration In linear motion Fnet = m a In circular motion Fc = m Ac
+ Centripetal Force & Acceleration m Fc v Ac = v 2 / r Fc = m Ac Fc = m v 2 / r Fg
+ Centripetal Force & Acceleration v m Fc Ac = v 2 / r Fc = m Ac Fc = m v 2 / r
+ Centripetal Force & Acceleration Centripetal Force Centripetal force is a force directed toward the center of the circle Fc = m Ac = 2 mv /r = mr 2
+ Centripetal Force Exercise Centripetal Force (Fc): Linear speed = 4 m/s 2 m 2 kg Centripetal Force = ?
+ Centripetal Force Exercise Centripetal Force (Fc): Angular speed = 3 rad/s 2 m 5 kg Centripetal Force = ?
+ Centripetal Force & Acceleration Centripetal Force Centripetal force is directly proportional to mass (m) Fc ~ m (Fc = m Ac = mv 2/r = mr 2)
+ Centripetal Force & Acceleration Centripetal Force Centripetal force is directly proportional to radius (r) Fc ~ r (Fc = m Ac = mv 2/r = mr 2)
+ Centripetal Force & Acceleration Centripetal Force Centripetal force is directly proportional to linear speed squared (v 2) Fc ~ 2 v (Fc = m Ac = mv 2/r = mr 2)
+ Centripetal Force & Acceleration Centripetal Force Centripetal force is directly proportional to angular speed squared ( 2) Fc ~ � 2 (Fc = m Ac = mv 2/r = mr 2)
+ Centripetal Force Example n For a circular motion, what if mass is doubled? Fc will be ………… n For a circular motion, what if radius is doubled? Fc will be ………… n For a circular motion, what if linear speed is doubled? Fc will be ………… n For a circular motion, what if angular speed is doubled? Fc will be …………
+ Centripetal Force Example n For a circular motion, what if mass is halved? Fc will be ………… n For a circular motion, what if radius is halved? Fc will be ………… n For a circular motion, what if linear speed is halved? Fc will be ………… n For a circular motion, what if angular speed is halved? Fc will be …………
+ Centripetal Force Example A 280 kg motorcycle traveling at 32 m/s enters a curve of radius = 130 m. What force of friction is required from the contact of the tires with the road to prevent a skid?
+ Centripetal Force Example A 280 kg motorcycle traveling at 32 m/s enters a curve of radius = 130 m. What force of friction is required from the contact of the tires with the road to prevent a skid? Fc = 280 kg x (32 m/s)2/130 m = 2205 N
+ Centripetal Force Exercise Astronauts are trained to tolerate greater acceleration than the gravity by using a spinning device whose radius is 10. 0 m. With what linear speed and rotational speed would an astronaut have to spin in order to experience an acceleration of 3 g’s at the edge of the device?
+ Centripetal Force Exercise To swing a pail of water around in a vertical circle fast enough so that the water doesn’t spill out when the pail is upside down. If Mr. Lin’s arm is 0. 60 m long, what is the minimum speed with which he can swing the pail so that the water doesn’t spill out at the top of the path?
+ Centripetal Force Exercise At the outer edge of a rotating space station, 1 km from its center, the rotational acceleration is 10. 0 m/s 2. What is the new weight of a 1000 N object being moved to a new storage room which is 500 m from the center of the space station?
+ Summary n Rotation & revolution n Period & frequency n Linear/tangential speed: v = Δd / Δt = 2πr / T = 2πrf (m/s) n Rotational/angular speed: �= 2π/T = 2πf n Tangential (rads/s) speed = Radius x Rotational speed: v = r�
+ Summary n Centripetal force & acceleration n Centripetal acceleration: Ac = v 2 / r = r 2 n Centripetal force: Fc = m Ac = mv 2/r = mr 2 n Centripetal force: Fc ~ m n Centripetal force: Fc ~ r n Centripetal force: Fc ~ v 2 n Centripetal force: Fc ~ 2
+ Centripetal Force Lab
+ Centripetal Force Lab
+ Centripetal Force Lab m Fc Fg v
+ Centripetal Force Lab m Fc v Ac = v 2 / r Fc = m Ac Fc = m v 2 / r Fg
+ Centripetal Force Lab
+ Centripetal Force Lab
+ Centripetal Force Lab Common Errors n The position of clip n The plane of circular motion n The washers are not identical
- Equations of motion rotation about a fixed axis
- Pitch factor formula
- Direct axis and quadrature axis
- Axis 1 and axis 2 disorders
- Conjugate axis of hyperbola
- Conic sections table
- Axis 1 and axis 2 disorders
- Tetrahedron axis of rotation
- Improper rotation axis
- Nature of roots examples
- Fixed axis rotation
- S2n axis
- Axis of rotation
- Improper rotation axis
- Rotation axis
- Circular movement around an axis
- Optical rotation slideshare
- Create length and height in hair design
- Seasons
- Video on rotation and revolution
- What causes night and day
- Rotation and revolution
- Radiation convection and conduction
- Earth from moon
- Revolution vs rotation
- Define rotation and revolution
- Rotation versus revolution
- Whats the difference between rotation and revolution
- Define moon phases
- Axes of movement
- Russian revolution vs french revolution
- Did american revolution cause french revolution
- Modern commercial agriculture
- In plane motion the rotation and translation would be
- Relativistic circular motion
- Circular motion lab
- Circular motion formula
- Non uniform circular motion
- Learning objectives for newton's laws of motion
- Circulatory motion
- Acceleration formula in circular motion
- Rounding car
- Two examples of circular motion
- Rotor ride physics
- Circular motion formula
- Angular velocity formula
- Example of circular motion
- Conceptual physics chapter 9 circular motion answers
- Chapter 10 circular motion
- Tension in a circular motion
- Chapter 5 circular motion gravitation
- Circular motion
- Ucm gravity
- Circular motion
- Circular motion
- To mix foods lightly with a lifting motion
- Maximum velocity in vertical circular motion
- Circular motion conceptual questions
- Circular motion
- Dynamics of uniform circular motion
- Si unit of circular motion
- Ap physics unit 3 circular motion and gravitation
- Ap physics circular motion
- Effects of looping the loop in circular motion
- V=2πr
- A circular motion is one dimensional
- Acceleration vector projectile motion
- Physics textbook
- Constant speed circular motion