Rotational Kinematics Worksheet 1 Conversions: 1) Given a circle or circular path with a radius of 25 cm, convert the following to linear distances: 1.5 radians, 6.0 radians, 1.6 x 104 radians 2) Given a circle or circular path with a radius of 5.0 x 10-5 m, convert the following to radial distances: 2.5 x 10-5 m, 1.0 x 10-3 m, 5.0 m 3) For 2) through how many circles were completed for each distance? 4) What is the angular and linear velocity of the second hand of clock? Minute hand? Hour hand? 5) Convert the following to first angular and then tangential velocity: a. A disc with a diameter of 10.0 cm spinning at 5000. RPM (Revolutions per minutes) b. A baton with a length of 0.50 m is spun about its center at 200. RPM. 6) What is the period of rotation for each of the following? a. r = 0.125, 6.0 b. r = 2.5, 15 c. r = 0.50, 950° per second 7) Given , a. b. c. d. e. f. g. Which way is the object initially spinning? How long before it switches directions? What is the period of rotation, initially? What is the tangential velocity after 20.0 s given a radius of 2.0 m? Given d) How many degrees has it rotated through? What is the initial centripetal acceleration given a radius of 3.0 m? Given f) Does the centripetal acceleration change with time? Prove it. What is the centripetal acceleration after 5.0 s? 8) You are pulling on a thread that is being unwound from a spool that has a diameter of 2.54 cm. The thread is unwinding tangentially relative to the spool. You are pulling in such a way that the thread is getting longer at a constant rate by 6.0 cm every 2.0 s. a. What is the tangential velocity? Angular velocity? b. What is the tangential acceleration? Centripetal acceleration? Net acceleration? c. Now, you apply a constant force for 2.5 s such that the new angular velocity is 3.6 . During this time, what is the magnitude of ? d. Given c) how much thread has unspooled during the 2.5 s? 9) You are a DJ spinning some vinyl, old school. The turntable rotates clockwise at 78 rpm. A small piece from a purple feather boa lands such that it lies on a radial line at θ = 0.45 rad at t = 0 s. Where is the piece of the boa found after 8.0 s? Remember, the answer is not about total distance, but about the angle with respect to 0 radians after 8.0 s.

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