Uniform circular motion (UCM) refers to motion at a constant speed in a circular path. For an object to move in UCM, it must experience a net force towards the center of the circle, known as the centripetal force. This force can be provided by tension, normal force, gravity, or friction. To solve a UCM problem, identify the known values such as speed, radius, and mass and use the equations for velocity, centripetal acceleration, and centripetal force to determine the net force required.

1. Uniform Circular Motion

2. What is UCM?

3. U C M niform

4. U C M niform same speed

5. U C M ircular

6. U C M otion

7. Centripetal Force

8. Centripetal Force F net making object move in UCM

10. F c =Tension

12. F c =Normal Force

14. F c =Gravity

16. F c =Friction

17. An object in UCM is accelerating

18. An object in UCM is accelerating always

19. An object in UCM is accelerating toward the center of the circle always

20. How to Solve a UCM Problem

21. Write out the knowns

22. Identify force(s) causing the object to move in UCM

23. An Example of How to Solve a UCM Problem

24. For the sake of this problem, we are going to assume that Glaz finally snaps and starts doing doughnuts in the parking lot. The radius of these doughnuts is 15m, and it takes her 5 seconds to do each. We are going to try and find her centripetal force.

25. You can tell this is a physics problem since the situation it presents is impossible; we all know Glaz snapped YEARS ago.

26. Oh, and we also won’t be taking into account silly little things like friction.

27. But forget about that, lets list our knowns. v=? T= 5secs a c =? r= 15m M=1100kg As you can see, we don’t know much.

28. In order to solve this problem we’re going to have to use three equations.

29. Velocity v=2πr/t Centripetal Acceleration A c =v^2/r Centripetal Force F c =ma c

30. Let’s start with velocity: Formula: v=2πr/t Formula with substitutions: 2π(15m)/5 secs Answer: 18.84955592m/s

31. Now we’ll move on to centripetal acceleration. Formula: A c =v^2/r Formula with substitutions: A c =(18.84955592m/s)^2/15m Answer: A c =23.68705056m/s^2

32. And finally we have enough data to calculate centripetal force. Formula: F c =ma c Formula with substitutions: 1100kg(23.68705056m/s^2) Answer: 26055.75561N

33. So as you can clearly see, UCM equations are quick, easy, and (generally) painless to do!