Newton’s second law for rotation

Definition

Newton’s second law for rotation states that the net torque acting on an object is equal to the product of its moment of inertia and angular acceleration. Mathematically, it is expressed as $\tau = I \alpha$.

5 Must Know Facts For Your Next Test

1. Net torque ($\tau$) is the rotational equivalent of net force in linear motion.
2. Moment of inertia ($I$) depends on the mass distribution relative to the axis of rotation.
3. Angular acceleration ($\alpha$) is measured in radians per second squared ($\text{rad/s}^2$).
4. $\tau = I \alpha$ can be used to calculate any one of these variables if the other two are known.
5. The direction of angular acceleration follows the right-hand rule.

Review Questions

• What is the mathematical expression for Newton’s second law for rotation?
• How does moment of inertia affect an object's resistance to changes in its rotational motion?
• In what units is angular acceleration measured?

Related terms

Torque: A measure of how much a force acting on an object causes that object to rotate, calculated as $\tau = rF \sin(\theta)$ where $r$ is the lever arm and $F$ is the applied force.

Moment of Inertia: A scalar quantity representing an object's resistance to change in rotational motion, depending on both its mass and distribution around the axis.

Angular Acceleration: The rate at which an object's angular velocity changes with time, typically measured in radians per second squared ($\text{rad/s}^2$).