6 Angular Momentum Free Online FlashCards

How is a particle’s angular momentum defined?

For a particle, angular momentum is $\mathbf L=\mathbf r\times\mathbf p$, where $\mathbf p=m\mathbf v$.

How do you determine the direction of angular momentum?

It points perpendicular to the plane containing $\mathbf r$ and $\mathbf p$, in the direction given by the right-hand rule.

What is the SI unit of angular momentum?

The SI unit is $\mathrm{kg\,m^2/s}$.

How is net torque related to angular momentum?

Torque is $\boldsymbol\tau=\mathbf r\times\mathbf F$, and the net torque satisfies $\frac{d\mathbf L}{dt}=\boldsymbol\tau_{\text{net}}$.

What determines the change in a system’s total angular momentum?

A system’s total angular momentum is the vector sum of its particles’ angular momenta. Its rate of change equals the net external torque; internal torques cancel for an isolated system under usual Newtonian assumptions.

What is angular momentum for a rigid body rotating about a fixed axis?

For rotation about a fixed axis, angular momentum along that axis is $L=I\omega$, where $I$ is the moment of inertia and $\omega$ is angular velocity.

Does angular momentum always point along angular velocity?

In general three-dimensional rotation, angular momentum need not point in the same direction as angular velocity. The scalar relation $L=I\omega$ applies for rotation about a principal axis or a constrained fixed axis.

When is a system’s total angular momentum conserved?

If the net external torque is zero, total angular momentum remains constant: $\mathbf L_{\text{initial}}=\mathbf L_{\text{final}}$.

What conservation equation applies to fixed-axis rotation?

For fixed-axis rotation with negligible net external torque, $I_i\omega_i=I_f\omega_f$. A change in moment of inertia can therefore change angular speed.

Does conserving angular momentum require conserving rotational kinetic energy?

No. A skater can increase rotational kinetic energy by pulling in their arms and doing muscular work, even while angular momentum is conserved.

Why is angular momentum conserved for a particle under a central force?

A central force has zero torque about its fixed center, so a particle’s angular momentum about that center is conserved even as its distance and speed vary.

What is precession in a spinning object?

An external torque changes the direction of a spinning object’s angular momentum, producing a change in its spin-axis direction called precession.