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# UCM 5

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### UCM 5

1. 1. UNIFORM CIRCULAR MOTION
2. 2. What is UCM?
3. 3. <ul><ul><ul><li>UCM is the motion of an object along a circular path at a constant speed. </li></ul></ul></ul>
4. 4. So What Causes an Object to move in UCM?
5. 5. Centripetal force Causes an object to stay in UCM. <ul><li>Centripetal force is any force or sum of forces which keeps an object in UCM. </li></ul>
6. 6. REMEMBER! <ul><li>Centripetal acceleration and Centripetal force are directed to the center. </li></ul><ul><li>Velocity is directed tangentially to the curvature of motion. </li></ul>
7. 7. EXAMPLES OF UCM
8. 8. Car turning a corner
9. 9. Woman on a rotor
10. 10. Ball Spinning On String
11. 11. Satellite in UCM
12. 12. Steps for solving UCM problems
13. 13. Problem <ul><li>If Captain Crunch is flying his 60,500kg plane in a circle whose radius is 50km, Once every 30 minutes, what is the size of its centripetal force? </li></ul>
14. 14. Free body diagram
15. 15. Step 1 <ul><li>Write out formulas. </li></ul><ul><li>Fc=MAc </li></ul><ul><li>Ac=(v^2)/r </li></ul><ul><li>V=[2(pi)r]/T </li></ul>
16. 16. Step 2 <ul><li>Write knowns </li></ul><ul><li>M=60,500kg </li></ul><ul><li>r=50km=50000m </li></ul><ul><li>t=30min=1800sec </li></ul><ul><li>Fc=? </li></ul>
17. 17. Step 3 <ul><li>Put knowns into formula </li></ul><ul><li>V=[2(pi)50,000m]/1800sec </li></ul><ul><li>V=174.5m/s </li></ul><ul><li>Ac=[v^2]/r=[(174.5m/s)^2]/50000m </li></ul><ul><li>Ac=.609m/s^2 </li></ul><ul><li>Fc=mAc </li></ul><ul><li>Fc=60,500kg*.609m/s^2 </li></ul><ul><li>Fc=36845N </li></ul>
18. 18. Very Important! <ul><li>Centripetal force = mass x centripetal acceleration </li></ul><ul><li>Centripetal force is directed towards the center </li></ul>
19. 19. Don’t Forget! <ul><li>Centripetal acceleration is directed towards the center </li></ul><ul><li>Velocity is tangential to the path of motion </li></ul>
20. 20. Finally <ul><li>Make sure you draw free body diagrams! </li></ul><ul><li>They are VERY IMPORTANT!! </li></ul>