Download Circular Motion HW-4

Rotational Dynamics HW:
due______________
Just 7 Problems….
1.
The L-shaped object in Figure 1 consists of three masses connected by light rods. What net torque
must be applied to this object to give it an angular acceleration of 1.20 rad/s2 if it is rotated about
(a) the x axis, (b) the y axis, or (c) the z axis (which is through the origin & perpendicular to the
page)?
Figure 1
Figure 2
2. A net torque of 13 N·m is applied to the rectangular object shown in Figure 2. The torque can act
about the x axis, the y axis, or the z axis (which passes through the origin and points out of the page).
(a) In which case does the object experience the greatest angular acceleration? The least angular
acceleration? Explain.
Find the angular acceleration when the torque acts about (b) the x axis, (c) the y axis, and (d) the z
axis.
3. A wheel on a game show is given an initial angular speed of 1.22 rad/s. It comes to rest after rotating
through 3/4 of a turn. Find the average frictional torque (net torque) exerted on the wheel given
that it is a solid disk of radius 0.710 m and mass 6.40 kg.
4. A string of negligible mass is wound around a disk-shaped pulley of radius 0.121 m and
mass 0.742 kg. Hanging from the string is a 2.85-kg bucket. If the bucket is allowed to fall,
(a) what is it’s linear acceleration? (b) What is the angular acceleration of the pulley.
(c) What distance does the bucket drop in 1.50 seconds? (d) Is the tension in the string greater than,
less than, or equal to the weight of the bucket? Calculate the tension to verify your answer.
5. The two masses ( m1  5.0 kg and m2  3.0 kg ) in the Atwood’s machine shown in Figure 3 are released
from rest, with m1 at a height h = 0.75 m above the floor. When m1 hits the ground its speed is
1.8 m/s. Assuming that the pulley is a uniform disk with a radius of 12 cm, use conservation of
energy to find the mass of the pulley.
Figure 3
6. A solid ball (sphere) of mass 2.50 kg and radius of 0.0850 m is released from rest at the top of a ramp.
The ball rolls without slipping the entire length of the ramp. The top of the ramp is vertically 3.20
meters above the bottom of the ramp. (a) Look up the formula for, and calculate, the moment of
inertia of our ball. (b) Use conservation of mechanical energy to calculate the linear speed of the
ball at the bottom of the ramp. (c) Calculate the ball’s angular speed at the bottom of the ramp.
Figure 4
7. After you pick up a spare, your bowling ball rolls without slipping back toward the ball rack with a
linear speed of 2.85 m/s (Figure 4). To reach the rack, the ball rolls up a ramp that rises through a
vertical distance of 0.530 m. (a) What is the linear speed of the ball when it reaches the top of the
ramp? (b) If the radius of the ball were increased, would the speed found in part (a) increase,
decrease, or stay the same? Explain.
Answers
1. (a) 11 Nm (b) 12 Nm (c) 23 Nm
2. (a) Explain why  is greatest when torqued about the x-axis and least when torqued about the z-axis.
(b) 7.4 rad/s2
(c) 5.1 rad/s2
(d) 3.0 rad/s2
3. 0.255 Nm
4. (a) 8.67 m/s2 (b) 71.7 rad/s2 (c) 9.76 m (d) Explain … T = 3.22 N, Wbucket = 27.9 N
5. Mpulley = 2.15 kg
6. (a) 0.00723 kgm2 (b) 6.69 m/s (c) 78.7 rad/s
7. (a) 0.838 m/s (b) Explain why it would stay the same.