Circular Motion and the Law of Gravity

Angular Kinematics

Angular Kinematics s radian (rad) q r

Angular Kinematics Angular Displacement

Angular Kinematics Average angular Speed Instantaneous angular Speed

Angular Kinematics Average angular Acceleration Instantaneous angular Acceleration

Angular Kinematics Quantity Linear Angular Displacement x q Velocity v w Acceleration a a

Angular Kinematics Linear Equations Angular Equations

Angular Kinematics Angular and Linear Relationships

Centripetal Acceleration: v2 -v1 v2 Dq r2 Dr v1 Dq Divide by Time r1 Dv Uniform Circular Motion Simular Triangles

The speed of an object in Uniform Circular Motion m T r v M Mg

Motion in a vertical circle mg r At the top:

Motion in a vertical circle At the bottom: r T mg

Maximum Speed in turn N r m a fmax mg

Weight Reading on scale is the normal force N mg Scale

Apparent Weight at the Earth’s Surface At the North Pole: NN mg At the Equator: v NE mg

A space station is in the shape of a hollow ring 450 m in diameter. Gravity is simulated by rotating the ring. Find the speed in revolutions per minute needed in order to simulate the Earth’s gravity. R v N

v N

A 0.84 kg ball is attached to a vertical post by strings of length 1.2 m and 1.6 m. If the ball is set whirling in a horizontal circle. 1.2 m 1.6 m 0.84 kg

Find the minimum speed necessary for the lower string to be taut. q Tq Tx mg

Find the tension in each string if the ball’s speed is 5.0 m/s Tq q Tx mg

Newton’s Universal Law of Gravitation m1 m2 r Circular Motion and the Law of Gravity

Gravitational Force v m F R M

R = 7.40 x 106 m m ME = 5.98 x 1024 kg v Speed of a satellite

v Period of a Satellite m R = 7.40 x 106 m ME = 5.98 x 1024 kg

END ?