Which equation expresses torque as the rate of change of angular momentum?

Which equation expresses torque as the rate of change of angular momentum?

• A. tau_net = I * alpha
• B. tau_net = delta t / delta L
• C. tau_net = F r
• D. tau_net = delta L / delta t

Answer: (D)

Torque is the time rate of change of angular momentum. The angular momentum of a particle is L = r × p, so when a net external torque acts, L changes in time according to τ = dL/dt. In a discrete sense this is τ ≈ ΔL/Δt. The option that matches this idea uses ΔL/Δt, which directly expresses torque as how angular momentum evolves with time. The form τ = I α is a common rotational equation, but it’s a special case that applies when the moment of inertia is constant and the axis is fixed (and L = I ω). The ratio Δt/ΔL is the reciprocal and not the rate of change, and torque given by F r is missing the necessary cross product and isn’t generally correct.

Torque is the time rate of change of angular momentum. The angular momentum of a particle is L = r × p, so when a net external torque acts, L changes in time according to τ = dL/dt. In a discrete sense this is τ ≈ ΔL/Δt. The option that matches this idea uses ΔL/Δt, which directly expresses torque as how angular momentum evolves with time. The form τ = I α is a common rotational equation, but it’s a special case that applies when the moment of inertia is constant and the axis is fixed (and L = I ω). The ratio Δt/ΔL is the reciprocal and not the rate of change, and torque given by F r is missing the necessary cross product and isn’t generally correct.