PHYS 2001 Lecture : Chap 6 Notes
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Recall the following example from chapter 3: a ball is being twirled at speed (cid:9) on a string of length (cid:10). While the speed (cid:9) is constant, the velocity (cid:9)(cid:11) is not! (cid:19)(cid:9) (cid:3) (cid:20) but (cid:12)(cid:11) (cid:21) (cid:20) Speed is constant v arad around path: (cid:9) (cid:3) (cid:22)(cid:23)(cid:10) (cid:24) Period of the motion: (cid:12)(cid:13)(cid:14)(cid:15) (cid:3) (cid:9)(cid:16) (cid:10) (cid:17)(cid:18) (cid:24) (cid:3) (cid:22)(cid:23)(cid:10) (cid:9) This is all basic kinematics, and does not tell us what causes the ucm. Since there is an acceleration (cid:12)(cid:11)(cid:13)(cid:14)(cid:15) for the ball, newton"s 2nd law tells us that there must be some non-zero net force (cid:25)(cid:11)(cid:26)(cid:27)(cid:28). Ball on string, frictionless surface. (cid:25)(cid:31) (cid:25)(cid:11)(cid:26)(cid:27)(cid:28) (cid:3) ! (cid:25)(cid:11)(cid:13) (cid:3) (cid:29)(cid:12)(cid:11)(cid:13)(cid:14)(cid:15) (cid:24) (cid:29)(cid:30) Since only tension points inward, here tension is the centripetal force. The centripetal force is not a new force. It is the vector sum of all the radial forces acting during circular motion: (cid:25)(cid:11) should never appear on an fbd.
