2. Introduction to Uniform Circular Motion

3. Uniform Circular Motion An object moves at uniform speed in a circle of constant radius. Uniform circular motion is accelerated motion. Why?

4. Centrifugal Force It’s a myth! We need to go back to Newton’s Laws to properly explain the feeling you get on a merry-go-round or in a turning car.

5. When a car accelerates You, as a passenger, feel as if you are flung backward. Your inertia (mass) resists acceleration. You are NOT flung backward. Your body wants to remain at rest as the car accelerates forward.

6. When a car decelerates You, as a passenger, feel as if you are flung forward. Your inertia (mass) resists the negative acceleration. You are NOT flung forward. Your body wants to remain in motion at constant velocity as the car accelerates backwards.

7. When a car turns You feel as if you are flung to the outside. Your inertia resists acceleration. You are not flung out, your body simply wants to keep moving in straight line motion!

8. As a general rule Whenever you feel you are flung in a certain direction, you can bet the acceleration is pointing in the opposite direction. Remember the elevator problems? When you feel you are flying up, acceleration of the elevator is down. When you feel you are sinking down, acceleration is up.

9. Acceleration in Uniform Circular Motion The velocity vector at any given point is subjected to an acceleration that turns it, but does not speed it up or slow it down. The acceleration vector is always at right angles to the velocity. The acceleration points toward the center of the circle.

10. Acceleration in Uniform Circular Motion The acceleration responsible for uniform circular motion is referred to as centripetal acceleration.

11. Centripetal Acceleration a c = v 2 /r a c : centripetal acceleration in m/s 2 v: tangential speed in m/s r: radius in meters v acac v acac acac v Centripetal acceleration always points toward center of circle!

12. Force in Uniform Circular Motion A force responsible for uniform circular motion is referred to as a centripetal force. Centripetal force is simply mass times centripetal acceleration. F c = ma c

13. Centripetal Force F c = m a c F c = m v 2 / r F c : centripetal force in N v: tangential speed in m/s r: radius in meters v FcFc v FcFc FcFc v Always toward center of circle!

14. More on Centripetal Force Centripetal force is not a unique type of force. Centripetal forces always arise from other forces. You can always identify the real force which is causing the centripetal acceleration. Nearly any kind of force can act as a centripetal force.

15. Friction as centripetal force As a car makes a turn, the force of friction acting upon the turned wheels of the car provide the centripetal force required for circular motion.

16. Tension as centripetal force As a bucket of water is tied to a string and spun in a circle, the force of tension acting upon the bucket provides the centripetal force required for circular motion.

17. Gravity as centripetal force As the moon orbits the Earth, the force of gravity acting upon the moon provides the centripetal force required for circular motion.

18. Normal force as centripetal force An automobile turning on a banked curve uses the normal force to provide the necessary centripetal force.

19. Weight on a string moving in vertical circle Centripetal force arises from a combination of tension and gravity.

20. Tennessee Tornado at Dollywood Centripetal force when you are upside down arises from a combination of normal force and gravity.

21. Centripetal Force can do no work A centripetal force alters the direction of the object without altering its speed. Since speed remains constant, kinetic energy remains constant, and work is zero.

22. The Universal Law of Gravity F g = -Gm 1 m 2 /r 2 F g : Force due to gravity (N) G: Universal gravitational constant 6.67 x 10 -11 N m 2 /kg 2 m 1 and m 2 : the two masses (kg) r: the distance between the centers of the masses (m)

23. Acceleration due to gravity F g = mg = GmM E /r 2 What is g equivalent to? g = GM E /r 2

24. Acceleration and distance

25. PlanetRadius(mMass (kg)g (m/s2) Mercury2.43 x 10 6 3.2 x 10 23 3.61 Venus6.073 x 10 6 4.88 x10 24 8.83 Mars3.38 x 10 6 6.42 x 10 23 3.75 Jupiter6.98 x 10 6 1.901 x 10 27 26.0 Saturn5.82 x 10 7 5.68 x 10 26 11.2 Uranus2.35 x 10 7 8.68 x 10 25 10.5 Neptune2.27 x 10 7 1.03 x 10 26 13.3 Pluto1.15 x 10 6 1.2 x 10 22 0.61

26. Kepler’s Laws 1. Planets orbit the sun in elliptical orbits. 2. Planets orbiting the sun carve out equal area triangles in equal times. 3. The planet’s year is related to its distance from the sun in a predictable way.

27. Kepler’s Laws

28. Satellites

29. From geometry, we can calculate orbital speed at any altitude.

32. Orbital Motion Gm e m s / r 2 = m e v 2 / r = The mass of the orbiting body does not affect the orbital motion!

33. Geosynchronous satellite A geosynchronous satellite is one which remains above the same point on the earth. Such a satellite orbits the earth in 24 hours, thus matching the earth's rotation. How high must a geosynchronous satellite be above the surface? (M earth = 5.98x10 24 kg, R earth = 6.37 x 10 6 m)