Activity 12.5.1. The Ladder.
A ladder leans against a wall, as shown in the figure below. Draw an extended free body diagram for the ladder and describe the system using the Rotational Law of Motion (Newton’s 2nd Law for Rotation).
Section 12.5 Applications of Torque
Activity 12.5.2. Torque Direction.
For each situation described below, determine the sign of the net torque, the sign of the angular velocity, and the sign of the angular acceleration.
- Rotating counterclockwise faster and faster
- Rotating counterclockwise slower and slower
- Rotating clockwise faster and faster
- Rotating clockwise slower and slower
A*R*C*S 12.5.3. The Waterwheel.
A waterwheel is lowered into a river that exerts a constant force \(F\) to the right on the bottom of the wheel. How long does it take for the wheel to complete its first revolution?
Tip.
Describe the motion of the waterwheel and draw an extended free-body diagram.
Activity 12.5.4. Tug-of-War.
Two athletes are engaged in a modified game of Tug-of-War. Each athlete has a rope that is connected to a long wooden board with mass \(m\) that is free to rotate about its center, as shown in the figure.
(a)
If the wooden board does not rotate, how does the tension from athlete A compare to the tension from athlete B?
(b)
Which one will win if athlete B can exert a tension force that is 1.5 times bigger than athlete A? Write a symbolic expression for the board’s angular acceleration.
Tip.
Write the moment of inertia for the board in terms of given quantities by looking at a moment of inertia table. You will need to decide what kind of object to use as a model for the board and choose an appropriate axis of rotation.
A*R*C*S 12.5.5. Massive Pulley.
The pulley shown has mass \(m_3\text{.}\) Two bricks with mass \(m_1 \gt m_2\) are connected by a rope suspended over the pulley. The masses are released from rest. Determine the acceleration of each block.
Tip 1.
Analyze and Represent: Draw extended free-body diagrams for each object. Discuss your coordinate systems.
Tip 2.
Sensemake: Use special-case analysis and the fact that you have likely solved this problem before when the pulley is massless.
