Intro to Angular Momentum Practice Problems

When calculating Mars' angular momentum in a round orbit around the sun, is it reasonable to consider it as a point mass? (Useful data about Mars: mass: 6.42 × 10²³ kg; radius: 3.39 × 10⁶ m; orbit radius: 2.28 × 10¹¹ m; orbital period: 687.0 days)

A motor-driven floor scrubber has a mass of 1.5 kg and a diameter of 430 mm. The scrubber rotates about an axle attached to its center. The scrubber sweeps an angle as a function of time given by θ(t) = At² + Bt⁴. If θ is in radians, t in seconds, and A and B are equal to 0.820 and 0.710, respectively, determine the units of A and B.

Determine the angular momentum magnitude for Mars revolving around the sun, assuming a circular orbit. Treat Mars as a particle? (Useful data about Mars: mass: 6.42 × 10²³ kg; radius: 3.39 × 10⁶ m; orbit radius: 2.28 × 10¹¹ m; orbital period: 687.0 days)

A revolving gate has four arms at right angles that rotate about a central axis. Each arm has a mass of 8.20 kg and is 2.60 m long. A 59.0 kg vandal sits on the outer end of one of the arms and pushes against the wall, spinning the gate at 3.60 rev/s. Determine the angular momentum magnitude of the vandal-gate system. Treat the arms as uniform rods and the vandal as a point mass.

A bicycle wheel has a radius of 35 cm and a mass of 2.5 kg. If the wheel is set to spin at 300 rpm and is allowed to precess around a vertical axis, determine the precession period of the wheel. Assume the wheel is a cylindrical hoop.

A disc having a mass of 120 g and radius of 8.0 cm is set to spin at 800 rpm. The disc is attached to support through a massless rod such that the distance of the support is 'radius + 2.0' cm from the center of mass of the disc to pivot. Calculate the precession frequency of the disc in rpm.

Determine the angular momentum vector of a 3.0 kg spinning sphere rotating about its central axis as depicted in the figure below. Express your answer using appropriate unit vectors. Consider the radius of the sphere is 6 cm.

A 300 g rectangular slab is rotating about its centre as shown in the figure. Calculate the angular momentum vector of the slab. The slab is 30.0 cm long and 12.0 cm wide. Express the final answer using appropriate unit vectors.

A uniform cylindrical flywheel has a radius of 22 cm and mass of 3.2 kg and is rotating at a rate of 1600 rpm. Calculate what the values of the angular momentum and the required torque will be in order to make the flywheel come to a stop in 8.0 s.

An electron moves in a helical trajectory within a uniform magnetic field oriented along the y-axis. The position of the electron is described by the vector

$\begin{array}{l}\vec{r}=b\cos \left(\frac{2\pi y}{c}\right)\hat{\mathbf{i}}+y\ \hat{\mathbf{j}}+b\sin (\frac{2\pi y}{c})\hat{\mathbf{\ k}}\end{array}$

where $b$ represents the radius of the helical path, $c$ denotes the pitch of the helix, and $y$ varies as $y=v_{y}t$ , where $v_{y}$ is the constant component of velocity along the $y-axis$. Determine the time-dependent angular momentum $\vec{L}$ of the electron about the origin.