1. Circular Motion and
the Law of Gravity

2. Angular Kinematics

3. Angular Kinematics s
radian (rad) q r

4. Angular Kinematics
Angular Displacement

5. Angular Kinematics
Average angular Speed
Instantaneous angular Speed

6. Angular Kinematics
Average angular Acceleration
Instantaneous angular Acceleration

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

8. Angular Kinematics
Linear Equations
Angular Equations

9. Angular Kinematics
Angular and Linear Relationships

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

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

12. Motion in a vertical circlemg r
At the top:

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

14. Maximum Speed in turn N r m a
fmax mg

15. Weight
Reading on scale
is the normal force N mg
Scale

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

17. 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

18. v N

19. 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

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

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

22. Newton’s Universal Law of Gravitationm1 m2 r
Circular Motion and the Law of Gravity

23. Gravitational Force v m F R M

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

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

26. END ?