Rotational Motion Cheat Sheet

Key Definitions

• Angular Displacement: Change in angular position, measured in radians.

• Angular Velocity (\( \omega \)): Rate of change of angular displacement, measured in rad/s.

• Angular Acceleration (\( \alpha \)): Rate of change of angular velocity, measured in rad/s².

• Moment of Inertia (\( I \)): Measure of an object's resistance to changes in its rotation, depends on mass distribution.

Important Concepts

Rotational Kinematics

• Analogous to linear motion; uses angular variables.

• Equations of motion for rotation:

• θ = ω₀t + 0.5αt²

• ω = ω₀ + αt

Torque

• Torque (\( τ \)): τ = r × F

• \( r \): lever arm (distance from pivot)

• \( F \): applied force

• Direction determined by the right-hand rule.

Equilibrium

• Static Equilibrium: Sum of forces and torques must be zero.

• ΣF = 0

• Στ = 0

Key Formulas

• Moment of Inertia: I = Σmr²

• Rotational Kinetic Energy: KE_rot = 0.5Iω²

• Newton's Second Law for Rotation: τ = Iα

Common Mistakes to Avoid

Common Mistake: Confusing angular and linear quantities (e.g., \( v \) with \( ω \)). Remember: \( v = rω \).

Memory Tricks

Tip: "TANGENT" —

• Torque

• Angular Displacement

• Newton's Second Law

• Gravity (affects torque)

• Equilibrium

• Net torque

• Time (in rotational equations)

Key Diagrams

   Torque (τ)
    |
    |     
    |       F
    |      ↗
    |     ↗
    |    ↗
    |   ↗
    |  ↗
    | ↗
    |/_________ r