PHYS 2211 Module 10 Self Assessment Practice Problems

Module 10 Self Assessment Practice Problems


The angular position of a rod varies as radians from time t = 0. The rod has two beads on it as shown in the figure, one at 10 cm from the rotation axis and the other at 20 cm from the rotation axis.
(a) What is the instantaneous angular velocity of the rod at t = 5 s?
(b) What is the angular acceleration of the rod?
(c) What are the tangential speeds of the beads at t = 5 s?
(d) What are the tangential accelerations of the beads at t = 5 s?
(e) What are the centripetal accelerations of the beads at t = 5 s?
Answer: (a) 200 rad/s (b) 40 rad/s2 (c) 20.0 m/s, 40.0 m/s (d) 4.0 m/s2, 8.0 m/s2 (e) 4000 m/s2, 8000 m/s2

A system of point particles is shown in the figure. Each particle has mass 0.3 kg and they all lie in the same plane.
(a) What is the moment of inertia of the system about the given axis?
(b) If the system rotates at 5 rev/s, what is its rotational kinetic energy?
Answer: (a) 0.168 kg•m2 (b) 82.9 J

A system consists of a disk of mass 2.0 kg and radius 50 cm upon which is mounted an annular cylinder of mass 1.0 kg with inner radius 20 cm and outer radius 30 cm. The system rotates about an axis through the center of the disk and annular cylinder at 10 rev/s.
(a) What is the moment of inertia of the system?
(b) What is its rotational kinetic energy?
Answer: (a) 0.315 kg•m2 (b) 621.8 J

Using the parallel axis theorem, what is the moment of inertia of the rod of mass m about the axis shown?
Answer: (7/36)mL2

Calculate the torque about the z-axis that is out of the page at the origin in the figure, given that F1 =3 N, F2 = 2 N, F3 = 3 N, and F4 = 1.8 N.
Answer: -8.92 N•m
A flywheel (I = 50 kg•m2) starting from rest acquires an angular velocity of 200.0 rad/s while subject to a constant torque from a motor for 5 s.
(a) What is the angular acceleration of the flywheel?
(b) What is the magnitude of the torque?
Answer: (a) 40.0 rad/s2 (b) 2000 N•m
A uniform cylindrical grinding wheel of mass 50.0 kg and diameter 1.0 m is turned on by an electric motor. The friction in the bearings is negligible.
(a) What torque must be applied to the wheel to bring it from rest to 120 rev/min in 20 revolutions?
(b) A tool whose coefficient of kinetic friction with the wheel is 0.60 is pressed perpendicularly against the wheel with a force of 40.0 N. What torque must be supplied by the motor to keep the wheel rotating at a constant angular velocity?
Answer: (a) 3.93 N•m (b) 12 N•m

The cart shown moves across the table top as the block falls. What is the acceleration of the cart? Neglect friction and assume the following data: m1 = 2.0 kg, m2 = 4.0 kg, I = 0.4 kg•m2, r = 20 cm
Answer: 1.23 m/s2
A clay cylinder of radius 20 cm on a potter’s wheel spins at a constant rate of 10 rev/s. The potter applies a force of 10 N to the clay with his hands where the coefficient of friction is 0.1 between his hands and the clay. What is the power that the potter has to deliver to the wheel to keep it rotating at this constant rate?
Answer: 12.6 W
An athlete in a gym applies a constant force of 50 N to the pedals of a bicycle at a rate of the pedals moving 60 rev/min. The length of the pedal arms is 30 cm. What is the power delivered to the bicycle by the athlete?
Answer: 94 W