AP Physics 1 Unit 5 Cheatsheet: Torque and Rotational Dynamics

Angular displacement: Δθ = θ − θ₀ (radians)

Average angular velocity: ω_avg = Δθ/Δt

Average angular acceleration: α_avg = Δω/Δt

For constant angular acceleration:

• ω = ω₀ + αt
• θ = θ₀ + ω₀t + ½αt²
• ω² = ω₀² + 2α(θ − θ₀)

Key insight: Angular kinematics mirrors linear kinematics. Use graphs of θ vs. t, ω vs. t, and α vs. t the same way you use position, velocity, and acceleration graphs—slopes and areas reveal relationships.

Equation: α_sys = Στ / I_sys = τ_net / I_sys

Meaning:

• Angular acceleration is directly proportional to net torque
• Angular acceleration is inversely proportional to rotational inertia
• Direction of α matches direction of τ_net

When to use: Whenever net torque ≠ 0, the system's angular velocity is changing.

Combined analysis: Some problems require both linear (ΣF = ma) and rotational (Στ = Iα) equations applied independently to fully describe the system.

Confusion 1: Forgetting that only the perpendicular component of force creates torque. A force along the position vector (θ = 0°) creates zero torque.

Confusion 2: Mixing up rotational inertia with mass. I depends on both mass and how far it is from the axis (I ∝ r²).

Confusion 3: Assuming rotational and translational equilibrium always occur together. They are independent—check Στ and ΣF separately.

Confusion 4: Forgetting sign conventions. Establish + and − directions for torque and angular quantities at the start.

Quick check: Units of τ are N·m; units of I are kg·m²; units of α are rad/s². Verify τ/I gives rad/s².