Torque, rotational inertia and rotational dynamics

Learning objectives

Calculate the torque exerted by a force as τ = rF sin θ, identify the lever arm, and assign a sign according to the sense of rotation the torque would produce

Explain that rotational inertia depends on the mass of a body and on how that mass is distributed about the axis, and calculate it for point masses using I = Σmr²

Apply the parallel axis theorem and use given expressions for the rotational inertia of common rigid bodies about an axis through the center of mass

Apply Newton's second law in rotational form, τ_net = Iα, including systems in which a string wound round a pulley couples rotational motion to translational motion

Apply the two conditions for static equilibrium, zero net force and zero net torque, to problems such as a supported beam or a ladder against a wall, choosing a convenient axis to eliminate an unknown

Design an experiment to determine the rotational inertia of an object from measurements of torque and angular acceleration, and evaluate the main sources of uncertainty