Fixed-Axis Rotational Dynamics: Torque, Inertia, and Angular Acceleration

All flashcards

State Newton’s second law for rotation.

For a rigid body rotating about a fixed axis, the signed net torque is $\tau_{net}=I\alpha$, where $I$ is the moment of inertia and $\alpha$ is angular acceleration.

How does tangential acceleration connect to angular acceleration?

For a point at radius $r$, the tangential acceleration magnitude is $a=r\alpha$.

What is the moment of inertia of a point particle?

For a particle of mass $m$ at perpendicular distance $r$ from the axis, $I=mr^2$.

What do torque and moment of inertia correspond to in linear dynamics?

Torque corresponds to force, while moment of inertia corresponds to mass; angular acceleration corresponds to linear acceleration.

What determines the sign of angular acceleration?

The sign of the net torque under the selected rotational sign convention determines the sign of angular acceleration. With counterclockwise positive, a positive net torque produces positive angular acceleration.

Quiz questions

1. Which equation gives Newton’s second law for a rigid body rotating about a fixed axis?Answer: $\tau_{net}=I\alpha$
2. A point particle has mass $m$ and is at distance $r$ from an axis. What is its moment of inertia?Answer: $I=mr^2$
3. In rotational dynamics, which quantity plays the role of mass in linear dynamics?Answer: Moment of inertia
4. If net torque stays constant while moment of inertia doubles, how does angular acceleration change?Answer: It becomes half as large.
5. With counterclockwise defined as positive, what is the sign of angular acceleration when net torque is positive?Answer: Positive, corresponding to counterclockwise acceleration.