Work, Energy, and Power in Fixed-Axis Rotation

All flashcards

Work by variable torque

For rotation from $\theta_A$ to $\theta_B$, $W=\int_{\theta_A}^{\theta_B}\tau_{\text{net}}\,d\theta$.

Rotational work-energy theorem

Net work on a rigid body rotating about a fixed axis equals its change in rotational kinetic energy.

Rotational kinetic energy

For rotation about a fixed axis, $K=\frac{1}{2}I\omega^2$.

Rotational power

For rotation about a fixed axis, instantaneous power is $P=\tau\omega$.

Work from a no-slip string

For string force $F$ and travel distance $d$, work on the pulley is $W=Fd=\tau\theta$.

Quiz questions

1. How is work calculated when net torque varies with angular position?Answer: Integrate net torque with respect to angular displacement.
2. A flywheel turns through eight complete revolutions. What angular displacement is this in radians?Answer: $16\pi\,\text{rad}$
3. A string unwinds without slipping from a pulley of radius $R$. If it travels distance $d$, which relation connects this travel to the pulley’s angular displacement $\theta$?Answer: $d=R\theta$
4. What is the torque about an axle from a force whose line of action passes through the axle?Answer: Zero, because the force has zero lever arm.
5. For rotation about a fixed axis, which equation gives instantaneous power from torque and angular velocity?Answer: $P=\tau\omega$