Problem — True or false on angular momentum and inertia

Problem

True or false? (a) The angular momentum of an isolated system is conserved. (b) The moment of inertia depends only on mass. (c) A force with zero arm generates no torque. (d) Pure rolling motion is equivalent to a rotation about the contact point. (e) Two bodies with the same mass always have the same moment of inertia.

Solution

(a) True. Without external torques, $L$ is conserved.

(b) False. It also depends on the distribution of the mass and on the chosen axis: $I = \sum m_i r_i^2$.

(c) True. If the arm is zero, $\tau = F\,r\sin\theta = 0$: the line of action passes through the pole.

(d) True. At each instant the contact point is at rest, so the motion is a pure rotation about that point (instantaneous axis of rotation).

(e) False. For equal mass, geometry changes $I$: a ring has a larger $I$ than a solid disc.

$\ev{\text{(a) T}\quad\text{(b) F}\quad\text{(c) T}\quad\text{(d) T}\quad\text{(e) F}}$

Links

Topics: Rotational dynamics Concepts: Conservation of angular momentum · Moment of inertia · Torque · Rolling