Torque and Work - AP Physics 1

Perpendicular distance from axis of rotation to line of action of force. The shortest distance determines the effectiveness of the applied force.

Total mechanical energy remains constant if only conservative forces act. Energy converts between kinetic and potential but total stays constant.

$P = F \cdot v \cdot \cos(\theta)$. Where $v$ is velocity and $\theta$ is angle between force and velocity vectors.

Joule (J). Work is energy transfer, measured in joules (force × distance).

Another term for lever arm. Moment arm and lever arm are synonymous terms in rotational mechanics.

Newton meter (N·m). Torque combines force and distance, so units are force × distance.

Work is the transfer of energy. Work changes an object's kinetic or potential energy state.

Torque is the rotational equivalent of force. Torque causes rotation just as force causes linear acceleration.

Torque is doubled. Torque is directly proportional to lever arm in the formula.

Causes angular acceleration. Net torque produces angular acceleration according to $\tau = I\alpha$.

$W = \tau \cdot \theta$. Where $\tau$ is torque and $\theta$ is angular displacement in radians.

$P = 40 \text{ W}$. $P = \frac{200}{5} = 40$ W.

Torque is doubled. Torque is directly proportional to lever arm in the formula.

$W = 15 \text{ J}$. $W = 5 \times 3 \times \cos(0°) = 15$ J.

Moment of inertia. Moment of inertia measures resistance to angular acceleration.

$U = mgh$. Potential energy depends on mass, gravity, and height above reference.

Work done on an object equals change in kinetic energy. Net work equals the change in kinetic energy of the object.

$P = F \cdot v \cdot \cos(\theta)$. Where $v$ is velocity and $\theta$ is angle between force and velocity vectors.

$W = F \cdot d \cdot \cos(\theta)$. Where $F$ is force, $d$ is displacement, and $\theta$ is angle between them.

Total mechanical energy remains constant if only conservative forces act. Energy converts between kinetic and potential but total stays constant.

$W = 100 \text{ J}$. $W = P \times t = 50 \times 2 = 100$ J.

$\tau = I\alpha$. Relates torque to moment of inertia and angular acceleration.

Net work is done by net force. Net work is the sum of work done by all forces acting.

$W = 40 \text{ J}$. $W = 10 \times 4 \times \cos(0°) = 40$ J.

Causes angular acceleration. Net torque produces angular acceleration according to $\tau = I\alpha$.

Net force and net torque must both be zero. Object neither translates nor rotates when all forces and torques balance.

$\cos(\theta) = 1$. When force and displacement are parallel, maximum work is done.

No change in rotational motion. Zero net torque means constant angular velocity (including zero).

Net torque must be zero. No net rotation occurs when clockwise and counterclockwise torques balance.