Rotational Mechanics Cheat Sheet
The core ideas of Rotational Mechanics distilled into a single, scannable reference — perfect for review or quick lookup.
PiqCue — piqcue.com/rotational-mechanics/cheatsheet
Quick Reference
Angular Position, Velocity, Acceleration
omega = d theta/dt, alpha = d omega/dt.
Torque
tau = r x F. Magnitude rF sin(theta).
Moment of Inertia
I = integral r^2 dm.
Rotational Second Law
tau_net = I alpha.
Parallel Axis Theorem
I = I_cm + Md^2.
Angular Momentum
L = I omega. Conserved when net torque = 0.
Rotational Kinetic Energy
KE_rot = (1/2)I omega^2.
Rolling Without Slipping
v_cm = R omega.
Key Terms at a Glance
Angular position (theta):The angle of rotation measured in radians from a reference direction.
Angular velocity (omega):Rate of change of angular position: omega = d theta/dt.
Angular acceleration (alpha):Rate of change of angular velocity: alpha = d omega/dt.
Torque (tau):Rotational analog of force. tau = r x F. Causes angular acceleration.
Moment of inertia (I):Rotational analog of mass. I = integral r^2 dm. Depends on mass distribution.
Parallel axis theorem:I = I_cm + Md^2. Relates I about CM to I about a parallel axis.
Angular momentum (L):L = I omega. Conserved when net external torque is zero.
Rotational kinetic energy:KE_rot = (1/2) I omega^2. Energy due to spinning motion.
Rolling without slipping:Condition where v_cm = R omega. No relative sliding at contact point.
Angular impulse:Integral of torque over time. Equals change in angular momentum.
Precession:Slow rotation of the spin axis of a gyroscope due to external torque.
Radius of gyration:k where I = Mk^2. Effective distance of mass from axis.
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