IB DP Physics 2025 SL&HL: 4.2 Rotational equilibrium and Newton’s second law Study Notes

Learning Objectives

Students should understand:
• the torque τ of a force about an axis as given by τ = Fr sin θ
• that bodies in rotational equilibrium have a resultant torque of zero
• that an unbalanced torque applied to an extended, rigid body will cause angular acceleration
• that the rotation of a body can be described in terms of angular displacement, angular velocity and angular acceleration
• that equations of motion for uniform angular acceleration can be used to predict the body’s angular position θ, angular displacement Δθ, angular speed ω and angular acceleration α, as given by

\(Δθ =\frac{ω_f + ω_i}{2}t\)

\(ω_f = ω_i + αt\)

\(Δθ = ω_it +\frac{1}{2} αt^2\)

\(ω_f^2 = ω_i^2 + 2αΔθ\)

• that the moment of inertia I depends on the distribution of mass of an extended body about an axis of rotation
• the moment of inertia for a system of point masses as given by \(I = Σmr^2\)
• Newton’s second law for rotation as given by τ = Iα where τ is the average torque
• that an extended body rotating with an angular speed has an angular momentum L as given by L = Iω
• that angular momentum remains constant unless the body is acted upon by a resultant torque
• that the action of a resultant torque constitutes an angular impulse ΔL as given by ΔL = τΔt = Δ(Iω),

• the kinetic energy of rotational motion as given by \(E_k=\frac{1}{2}Iω^2= \frac{L^2}{2I}\)