Chapter 10 Problems
1, 2, 3 = straightforward, intermediate, challenging
Section 10.1 Angular Position, Velocity, and Acceleration
1.During a certain period of time, the angular position of a swinging door is described by = 5.00 + 10.0t + 2.00t2, where is in radians and t is in seconds. Determine the angular position, angular speed, and angular acceleration of the door (a) at t = 0 and (b) at t = 3.00 s.
Section 10.2 Rotational Kinematics: Rotational Motion with Constant Angular Acceleration
2.A dentist's drill starts from rest. After 3.20 s of constant angular acceleration, it turns at a rate of 2.51 104 rev/min. (a) Find the drill's angular acceleration. (b) Determine the angle (in radians) through which the drill rotates during this period.
3.A wheel starts from rest and rotates with constant angular acceleration to reach an angular speed of 12.0 rad/s in 3.00 s. Find (a) the magnitude of the angular acceleration of the wheel and (b) the angle in radians through which it rotates in this time.
4.An airliner arrives at the terminal, and the engines are shut off. The rotor of one of the engines has an initial clockwise angular speed of 2 000 rad/s. The engine's rotation slows with an angular acceleration of magnitude 80.0 rad/s2. (a) Determine the angular speed after 10.0 s. (b) How long does it take the rotor to come to rest?
5.An electric motor rotating a grinding wheel at 100 rev/min is switched off. With
constant negative angular acceleration of magnitude 2.00 rad/s2, (a) how long does it take the wheel to stop? (b) Through how many radians does it turn while it is slowing down?
6.A centrifuge in a medical laboratory rotates at an angular speed of 3 600 rev/min. When switched off, it rotates 50.0 times before coming to rest. Find the constant angular acceleration of the centrifuge.
7.The tub of a washer goes into its spin cycle, starting from rest and gaining angular speed steadily for 8.00 s, at which time it is turning at 5.00 rev/s. At this point the person doing the laundry opens the lid, and a safety switch turns off the washer. The tub smoothly slows to rest in 12.0 s. Through how many revolutions does the tub turn while it is in motion?
8.A rotating wheel requires 3.00 s to rotate through 37.0 revolutions. Its angular speed at the end of the 3.00-s interval is
98.0 rad/s. What is the constant angular acceleration of the wheel?
9.(a) Find the angular speed of the Earth’s rotation on its axis. As the Earth turns toward the east, we see the sky turning toward the west at this same rate.
(b)The rainy Pleiads wester
And seek beyond the sea
The head that I shall dream of
That shall not dream of me.
–A. E. Housman (© Robert E. Symons)
Cambridge, England, is at longitude 0 and Saskatoon, Saskatchewan, is at longitude 107west. How much time elapses after the Pleiades set in Cambridge until these stars fall below the western horizon in Saskatoon?