Section 5.3: Torque
This section focuses entirely on torque, its calculation, and its effect on rotational motion.
Definition of Torque:
\( \tau = r F \sin\theta \)
- \( r \): Distance from axis of rotation
- \( F \): Force applied
- \( \theta \): Angle between force and lever arm
Torque is positive if it produces counterclockwise rotation, negative if clockwise.
Example 1
A wrench 0.3 m long has a force of 50 N applied perpendicular at its end. Find the torque.
\( \tau = r F \sin\theta = 0.3 \times 50 \times \sin 90° = 15 \, \text{N·m} \)
Example 2
Force of 30 N applied at 60° to lever arm of length 0.5 m. Find torque.
\( \tau = 0.5 \times 30 \times \sin 60° \approx 12.99 \, \text{N·m} \)
Practice Problems
- Force 40 N applied at 45° on 0.25 m wrench. Compute torque.
- Lever arm 1 m, force 20 N at 30°. Find torque.
- Torque needed for angular acceleration α = 5 rad/s² for disk I = 0.5 kg·m². Find required force at r = 0.2 m.
- Force 15 N applied perpendicular at 0.4 m. Find torque and direction.
- Force 60 N at 60° to 0.6 m arm. Compute torque magnitude.