Rotational Kinematics - AP Physics C: Mechanics

$\omega = \omega_0 + \alpha t$. Linear relationship between initial velocity, acceleration, and time.

$I = \frac{1}{2} m r^2$. Standard formula for uniform solid cylinder about central axis.

$\theta = 16$ rad. Using $\theta = \frac{1}{2}\alpha t^2$ when initial velocity is zero.

$\tau = I \alpha$. Rotational analog of $F = ma$ relating torque to angular acceleration.

$2\pi$ radians. One complete revolution equals $2\pi$ radians.

$\omega = 14$ rad/s. Using $\omega = \omega_0 + \alpha t$ with given values.

Moment of inertia. Mass determines linear inertia; moment of inertia determines rotational inertia.

Change of angular velocity per unit time. Rate of change of angular velocity, analogous to linear acceleration.

$v = r \omega$. Linear speed equals radius times angular velocity for circular motion.

$a_c = r \omega^2$. Acceleration directed toward center of circular motion.

$I = \frac{1}{2} m r^2$. Standard formula for uniform solid cylinder about central axis.

$\omega = 4\pi$ rad/s. 20 rev in 10 s = 2 rev/s = $2 \times 2\pi = 4\pi$ rad/s.

A measure of the force that can cause an object to rotate. Rotational analog of force that produces angular acceleration.

Radians. Base SI unit for angular position measurement.

$\tau = r F \sin \theta$. Cross product of position vector and force vector.

$\theta = \omega t$. Simplified formula when angular velocity is constant.

$\omega = 2\pi f$. Same as angular velocity formula in terms of frequency.

$W = \tau \theta$. Work equals torque times angular displacement in rotational motion.

Angular momentum. Conserved quantity in rotational motion, like linear momentum.

Newton meter (Nm). SI unit for rotational force measurement.

Radians. Base SI unit for angular position measurement.

$a_t = r \alpha$. Component of acceleration tangent to the circular path.

$\omega = 12$ rad/s. Angular velocity is $\frac{d\theta}{dt} = 6t$, so at $t = 2$ s: $\omega = 12$ rad/s.

Change of angular velocity per unit time. Rate of change of angular velocity, analogous to linear acceleration.

Radians per second (rad/s). Standard SI unit for rate of angular displacement change.

$\theta = \theta_0 + \omega_0 t + \frac{1}{2} \alpha t^2$. Kinematic equation analogous to $s = ut + \frac{1}{2}at^2$ for linear motion.

Newton meter (Nm). SI unit for rotational force measurement.

$\omega = 14$ rad/s. Using $\omega = \omega_0 + \alpha t$ with given values.

Angular momentum. Conserved quantity in rotational motion, like linear momentum.