By Valentina Tobos | Laurentiu Tobos

Updated on Sep 26, 2011

Review these concepts at: Rotational Equilibrium Study Guide

**Practice Questions**

- Which baseball bat has more rotational inertia, a long bat or a short bat?
- A young girl picks up an adult baseball bat. In order to bring the bat up to speed, where should the girl grab the bat—closer to the handle or closer to the more massive end? Explain briefly.
- Consider a ring and a cylinder of similar mass and radius. Which one will start moving first under an external influence? Explain briefly.
- Two objects have a cylindrical shape and the same mass, but one has a diameter twice as large as the other. How do the moment of inertia for the two objects compare?
- Two wooden dowels have the same mass and the same length, but one rotates about the center and the other about one of the ends. What is the ratio of the two moments of inertia? Explain.
- An object attached to a string is rotated in a circle and has a moment of inertia of
*I*= 0.1 N ·*m*^{2}and a mass of 400 g. Determine the diameter of the string.

- Consider standing by a door and trying to open it. In which case will the door open more easily: when you push on the door close to the door knob or when you push on the door close to the hinges (the strength of the push is the same in each case)? Explain briefly.
- In what direction are you going to apply a force on a door so that you get the maximum torque? Explain.
- What options do you have in order to get a zero torque even if you apply a force on an object? Explain.
- Is there a way to apply multiple nonzero forces on an object and obtain a zero torque? Explain.
- Consider a diving board at a swimming pool and a 65 kg person resting at the free end. What is the torque exerted on the board if its length is 250 cm?
- A rod is acted upon by a torque of 30 N · m, and a force of 12 N is acting at an angle 60° north of east with the rod as shown in Figure 9.12. Find the length of the lever arm and of the rod.
- Can you point to an example in the text of this lesson where two nonzero forces applied on the same object do not determine rotational motion?

- Both torque and mechanical work are equal to the product of a force and a distance. Are they different quantities? Why or why not? Explain briefly.
- Two people on each side of a door push at the same angle and with the same force on the door. Is it possible for one of them to be able to push the door against the other person?
- A uniform plank of mass
*m*= 20 kg is supported as shown in Figure 9.16. Why isn't the weight of the plank and its corresponding normal rotating the plank? - On a construction site, it is hoped that the plank (shown in Figure 9.17) of mass 8 kg will remain in equilibrium. Based on the diagram and data given, can you determine if a rotational equilibrium can be established? Use
- Is it possible for the system in Figure 9.18 to be in rotational equilibrium? The mass of the object is 2 kg, and its position on the board is fixed. The board is 2.2 m long, and the object is 0.3 m away from the pivot point.

**Answers**

- A longer one since
*I*~*L*^{2} - Closer to the massive end so that the distance to the axis of rotation is smaller and the bat has less inertia.
- The cylinder, since it has less inertia.
- The double diameter one has a moment of inertia four times larger.
- 1/4 since the one rotating around the center has a moment of
*m*·*L*^{2}/12 and the other is*m*·*L*^{2}/3 - 0.5 m
- By the door knob, since torque is then larger, and the effect on the door is larger, too.
- Perpendicular to the door plan.
- Apply force on the pivot point or along the lever arm.
- Apply them in different directions so that the torques cancel each other out.
- 1,625 N · m = 1,600 N · m
- 2.5 m and 5 m
- The one with the steering wheel in part B.
- Torque is associated with interaction, while work is associated with energy carried by an object.
- Yes, if one pushes farther from the pivot point than the other.
- Because they both act on the pivot point.
- Net torque is zero, so the system is in equilibrium.
- No, there is a net torque of 51 N · m.

From Physics Success in 20 Minutes A Day. Copyright © 2006 by LearningExpress, LLC. All Rights Reserved.

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