AP Physics 1 rotational motion intro study guide

Torque

A measure of the force that produces or changes rotational motion. $\displaystyle \tau = r \times F$.

Angular Velocity

Rate of change of angular displacement. $\displaystyle \omega = \\frac{\Delta \theta}{\Delta t}$.

True or False: Torque is a scalar quantity.

False, because torque is a vector quantity.

Moment of Inertia

Resistance of an object to change in its rotational motion, depends on mass distribution. $\displaystyle I = \sum m r^2$.

Difference between angular speed and linear speed.

Angular speed ($\displaystyle \omega$) relates to rotation, while linear speed ($\displaystyle v$) relates to distance traveled.

Centripetal Acceleration

Acceleration directed towards the center of a circular path. $\displaystyle a_c = \\frac{v^2}{r}$.

What is the formula for angular momentum?

$\displaystyle L = I \omega$, where $\displaystyle L$ is angular momentum, $\displaystyle I$ is moment of inertia.

Angular Displacement

The angle through which an object has rotated in a specified sense about a specified axis. $\displaystyle \Delta \theta$.

True or False: The units of torque are Nm.

True, because torque is measured in Newton meters.

What is the relationship between linear and angular quantities?

Linear speed $\displaystyle v = r \omega$, and linear acceleration $\displaystyle a = r \alpha$.

Rotational Kinetic Energy

Energy due to rotational motion. $\displaystyle KE_{rot} = \\frac{1}{2} I \omega^2$.

Difference between rotational and translational motion.

Translational motion is linear, while rotational motion involves rotation around an axis.

What is the formula for net torque?

$\displaystyle \tau_{net} = I \alpha$, where $\displaystyle \alpha$ is angular acceleration.

True or False: The moment of inertia depends on the axis of rotation.

True, because moment of inertia varies with the distribution of mass relative to the axis.

What is angular acceleration?

Rate of change of angular velocity. $\displaystyle \alpha = \\frac{\Delta \omega}{\Delta t}$.

Conservation of Angular Momentum

In an isolated system, the total angular momentum remains constant if no external torque acts.

What is the relationship between torque and angular acceleration?

$\displaystyle \tau = I \alpha$, showing that torque causes angular acceleration.

True or False: A larger radius decreases torque for a given force.

False, because torque increases with the radius for a constant force.

Equilibrium Condition

An object is in equilibrium when $\displaystyle \tau_{net} = 0$ and $\displaystyle \Sigma F = 0$.