Circular Motion - AP Physics C: Mechanics

$T = \frac{2\text{π}r}{v}$. Time for one complete revolution equals circumference divided by speed.

Rate of change of angular displacement. Rate at which angular displacement changes with time.

$\text{ω} = 5 \text{ rad/s}$. Using $\omega = \frac{v}{r} = \frac{10}{2} = 5$ rad/s.

Rate of change of angular displacement. Rate at which angular displacement changes with time.

$L = I\text{ω}$. Angular momentum equals moment of inertia times angular velocity.

$F_g = \frac{Gm_1m_2}{r^2}$. Newton's universal gravitation law for orbital mechanics.

$v = 5 \text{ m/s}$. Using $v = r\omega = 0.5 \times 10 = 5$ m/s.

$T = \frac{1}{f}$. Period and frequency are reciprocals of each other.

Towards the center of the circle. Centripetal acceleration always points radially inward.

$\text{ω} = \frac{2\text{π}}{T}$. Angular velocity equals $2\pi$ radians divided by period.

$a_r = \frac{v^2}{r}$. Radial acceleration component points toward the center of curvature.

The angle through which an object moves on a circular path. Angular measure of rotational motion in radians.

$a_t = r\text{α}$. Tangential acceleration equals radius times angular acceleration.

$F_c = 22.5 \text{ N}$. Using $F_c = \frac{mv^2}{r} = \frac{5 \times 9}{2} = 22.5$ N.

$a_c = 8 \text{ m/s}^2$. Using $a_c = \frac{v^2}{r} = \frac{4^2}{2} = 8 \text{ m/s}^2$.

$f = 0.2 \text{ Hz}$. Using $f = \frac{1}{T} = \frac{1}{5} = 0.2$ Hz.

Perpendicular to the plane of rotation. Angular velocity vector follows right-hand rule convention.

$I = mr^2$. Moment of inertia equals mass times radius squared for point mass.

$\tau = I\text{α}$. Torque equals moment of inertia times angular acceleration.

$\text{ω} = \frac{\text{π}}{1} \text{ rad/s}$. Using $\omega = \frac{2\pi \times 3}{6} = \pi$ rad/s.

Speed. Speed magnitude is constant while direction continuously changes.

Frictional force. Friction between tires and road provides the centripetal force.

The angle through which an object moves on a circular path. Angular measure of rotational motion in radians.

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

$a_c = \frac{v^2}{r}$. Acceleration directed toward the center, proportional to $v^2$ and inversely to radius.

$T = \frac{1}{f}$. Period and frequency are reciprocals of each other.

$F_c = \frac{mv^2}{r}$. Force equals mass times centripetal acceleration.

$F_{\text{net}} = ma_c$. Newton's second law applied to circular motion dynamics.

Towards the center of the circle. Centripetal acceleration always points radially inward.