Rotational Motion Cheatsheet

Cheat Codes & Shortcuts

• Definition: Rotational motion describes the movement of a body around a fixed axis.
• Angular Displacement: \( \theta \), measured in radians.
• Angular Velocity: \( \omega = \frac{d\theta}{dt} \), rate of change of angular displacement.
• Angular Acceleration: \( \alpha = \frac{d\omega}{dt} \), rate of change of angular velocity.
• Relation between linear and angular quantities: \( v = r\omega \), \( a_t = r\alpha \).
• Moment of Inertia: \( I = \sum m r^2 \), resistance to rotational acceleration.
• Torque: \( \tau = I\alpha \), rotational equivalent of force.
• Rotational Kinematic Equations (constant \( \alpha \)):
• \( \omega = \omega_0 + \alpha t \)
• \( \theta = \theta_0 + \omega_0 t + \frac{1}{2} \alpha t^2 \)
• \( \omega^2 = \omega_0^2 + 2\alpha(\theta - \theta_0) \)
• Rotational Kinetic Energy: \( K = \frac{1}{2} I \omega^2 \)

Quick Reference Table

Type	Form	Explanation
Angular Velocity	\( \omega = \frac{d\theta}{dt} \)	Rate of change of angular position
Angular Acceleration	\( \alpha = \frac{d\omega}{dt} \)	Rate of change of angular velocity
Torque	\( \tau = I \alpha \)	Causes rotational acceleration
Moment of Inertia	\( I = \sum m r^2 \)	Rotational inertia depends on mass distribution
Rotational KE	\( K = \frac{1}{2} I \omega^2 \)	Energy due to rotation
Kinematic Equation	\( \theta = \theta_0 + \omega_0 t + \frac{1}{2} \alpha t^2 \)	Angular displacement under constant acceleration

Advice

Rotational Motion Quick Tips

• Angular Velocity: Time derivative of angular displacement.
• Angular Acceleration: Time derivative of angular velocity.
• Torque: Product of force and lever arm, causes angular acceleration.
• Moment of Inertia: Depends on geometry and mass distribution.
• Kinematic Equations: Use rotational analogs of linear motion equations for constant angular acceleration.

Rotational Motion Speed Quiz

Test your speed with 5 rotational motion questions! You have 30 seconds per question.