Torque and Work - AP Physics C: Mechanics

Joule (J). Newton-meter equals one joule.

Newton-meter (N·m). Force times distance unit.

Work is the transfer of energy. Work changes the energy state of a system.

$p = 12, \text{kg} \cdot \text{m/s}$. Product of mass and velocity.

$J = \Delta p = F\Delta t$. Change in momentum equals force times time.

$J = 50, \text{N} \cdot \text{s}$. Force multiplied by time interval.

Angle between force vector and lever arm. Determines effective component of force for torque.

Perpendicular distance from axis of rotation to line of action of force. Distance that determines torque magnitude.

$W = F \times d \times \cos(\theta)$. Dot product of force and displacement vectors.

$p = mv$. Mass times velocity vector.

Watt (W). Joule per second equals one watt.

$\text{Efficiency} = \frac{\text{Useful Work Output}}{\text{Total Work Input}} \times 100%$. Ratio of useful output to total input.

A force with work independent of path taken. Gravity and springs are conservative forces.

$F_c = \frac{mv^2}{r}$. Inward force for circular motion.

Angular momentum. Rotational momentum is conserved without external torques.

$W = \tau \times \Delta \theta$. Rotational analog of $W = F \times d$.

Perpendicular distance from axis of rotation to line of action of force. Distance that determines torque magnitude.

Angle between force vector and lever arm. Determines effective component of force for torque.

Net work done equals change in kinetic energy. Fundamental theorem connecting work and motion.

Net torque must be zero. Sum of all torques equals zero for equilibrium.

$W = 80, \text{J}$. Force and displacement in same direction.

$P = \frac{W}{t}$. Rate at which work is done.

$P = 15, \text{W}$. Work divided by time interval.

Newton-meter (N·m). Force times distance unit.

$W = F \times d \times \cos(\theta)$. Dot product of force and displacement vectors.

$W_{net} = \Delta KE = \frac{1}{2}mv^2_f - \frac{1}{2}mv^2_i$. Net work equals change in kinetic energy.

Rate of energy transfer or conversion. How quickly energy is transformed.

Total mechanical energy remains constant if only conservative forces act. Sum of kinetic and potential energy stays constant.

Watt (W). Joule per second equals one watt.