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									Rotational Kinematics Whiteboarding Practice Problems

1) The disk in the figure is rotating about its central axis like a merry-go-round. The angular

position         of a reference line on the disk is given by


with t in seconds, in radian, and the zero angular position as indicated in the figure.
(a) Graph the angular position of the disk versus time from t = -3.0 s to t = 6.0 s. Sketch the disk
and its angular position reference line at t = -2.0 s, 0 s, and 4.0 s, and when the curve crosses the t

(b) At what time      does               reach the minimum value shown in the graph from (a)?
What is that minimum value?

(c) Graph the angular velocity        of the disk versus time from t = -3.0 s to t = 6.0 s. Sketch the

disk and indicate the direction of turning and the sign of       at t = -2.0 s and 4.0 s, and also at

(d) Use the results in parts (a) through (c) to describe the motion of the disk from t = -3.0 s to t =
6.0 s.

2) A grindstone rotates at constant angular acceleration                                    . At time t =

0, it has an angular velocity of                                  and a reference line on it is

horizontal, at the angular position                .

(a) At what time after t = 0 is the reference line at the angular position     = 5.0 rev?
(b) Describe the grindstone's rotation between t = 0 and t = 32 s.
(c) At what time t does the grindstone momentarily stop?
3) While operating a carnival ride called the Rotor (a rotating cylindrical ride), you spot a
passenger in acute distress and decrease the angular speed of the cylinder from 3.40 rad/s to 2.00
rad/s in 20.0 rev, at constant angular acceleration.
(a) What is the constant angular acceleration during this decrease in angular speed?
(b) How much time did the speed decrease take?

4) A cyclist traveling at 5.0 m/s uniformly accelerates up to 10.0 m/s in 2.0 s. Each tire of the bike
has a 35 cm radius, and a small pebble is caught in the tread of one of them. (a) What is the
angular acceleration of the pebble during those two seconds? (b) Through what angle does the
pebble revolve? (c) How far around the wheel does the pebble travel during that accelerating

5) In a microhematocrit centrifuge, small samples of blood are placed in heparinized capillary
tubes (heparin is an anticoagulant). The tubes are rotated at 11500 rpm, with the bottom of the
tubes 9.07 cm from the axis of rotation. (a) Find the linear speed of the tubes. (b) What is the
centripetal acceleration at the bottom of the tubes?

6) Suppose the centrifuge in Problem #5 is just starting up, and that it has an angular speed of

8.00 rad/s and an angular acceleration of                        . (a) What is the magnitude of the
centripetal, tangential, and total acceleration of the bottom of a tube? (b) What angle does the
total acceleration make with the direction of motion?

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