5 Rotational Motion Free Online FlashCards

How is angular displacement defined?

Angular displacement is the change in angular position: $\Delta\theta=\theta_2-\theta_1$.

How many radians are in one full revolution?

One full revolution is $2\pi$ radians.

What does angular velocity measure?

Angular velocity is the rate of change of angular position: $\omega=\frac{d\theta}{dt}$.

What does angular acceleration measure?

Angular acceleration is the rate of change of angular velocity: $\alpha=\frac{d\omega}{dt}$.

How does angular velocity change under constant angular acceleration?

For constant angular acceleration, angular velocity changes according to $\omega=\omega_0+\alpha t$.

How are tangential speed and angular velocity related?

A point at distance $r$ from the axis has tangential speed $v=r\omega$.

What is the radial acceleration of a rotating point?

Its inward radial acceleration is $a_r=r\omega^2$.

How do force and lever arm determine torque magnitude?

Torque magnitude is $\tau=rF\sin\phi=r_\perp F$, where $r_\perp$ is the perpendicular lever arm.

When is torque greatest, and when is it zero?

For a given force and distance, a perpendicular force produces the greatest torque; a force directed through the axis produces none.

What determines a system's moment of inertia?

For discrete particles, $I=\sum_i m_i r_i^2$. It depends on mass distribution and the chosen axis.

What is Newton's second law for rotation about a fixed axis?

For rotation about a fixed axis, the net torque satisfies $\sum\tau=I\alpha$.

What links translation and rotation in rolling without slipping?

Without slipping, the center-of-mass speed and acceleration satisfy $v_{\mathrm{CM}}=R\omega$ and $a_{\mathrm{CM}}=R\alpha$.