Torque describes how effectively a force causes an object to rotate about an axis. It matters in everyday systems such as doors, wrenches, bicycle wheels, gears, and motors. A force applied farther from the axis usually produces a larger rotational effect.
The direction of the torque determines whether the angular acceleration is clockwise or counterclockwise.
Key Facts
- Torque magnitude: tau = rF sin(theta), where theta is the angle between r and F.
- For a tangential force at the rim of a disk, tau = rF.
- Rotational form of Newton's second law: net tau = I alpha.
- Moment of inertia measures resistance to angular acceleration and depends on mass distribution.
- Angular acceleration is alpha = Delta omega / Delta t.
- For a solid disk rotating about its center, I = 1/2 MR^2.
Vocabulary
- Torque
- Torque is the turning effect of a force about an axis of rotation.
- Lever arm
- The lever arm is the perpendicular distance from the axis of rotation to the line of action of the force.
- Moment of inertia
- Moment of inertia is a measure of how difficult it is to change an object's rotational motion.
- Angular acceleration
- Angular acceleration is the rate at which angular velocity changes with time.
- Tangential force
- A tangential force acts along the tangent to a circular path and is perpendicular to the radius.
Common Mistakes to Avoid
- Using tau = rF for every force is wrong because only the perpendicular component of the force produces torque, so the general equation is tau = rF sin(theta).
- Confusing mass with moment of inertia is wrong because rotational acceleration depends on how the mass is distributed around the axis, not just the total mass.
- Ignoring the sign of torque is wrong because clockwise and counterclockwise torques oppose each other and must be added with direction in mind.
- Treating angular acceleration as linear acceleration is wrong because alpha is measured in rad/s^2, while linear acceleration is measured in m/s^2.
Practice Questions
- 1 A 20 N force is applied tangentially to the rim of a wheel with radius 0.40 m. What torque does the force produce about the center?
- 2 A solid disk has mass 6.0 kg and radius 0.50 m. A tangential force of 12 N is applied at the rim. Find the disk's moment of inertia and angular acceleration.
- 3 Two equal forces are applied to a door, one near the hinge and one near the handle, both perpendicular to the door. Explain which force produces more torque and why.