Rotating Systems: Energy & Momentum

A spinning disk has a moment of inertia $I$ and an angular velocity $\omega$. If the moment of inertia is doubled and the angular velocity is halved, what happens to the angular momentum?

A particle is moving in a circle. According to the right-hand rule, if the particle is moving counter-clockwise in the xy-plane, what is the direction of the angular momentum vector?

What physical quantity does the area under a torque vs. time graph represent?

Estimate the angular impulse on an object between $t = 0$ s and $t = 4$ s if the torque applied to the object varies with time according to the graph. Assume the graph is a triangle with base 4 and height 10.

A disk with a moment of inertia of $5 \text{ kg} \cdot \text{m}^2$ is rotating at a constant angular velocity of $2 \text{ rad/s}$. What is the magnitude of its angular momentum?

A projectile of mass $m$ is launched with an initial velocity $v_0$ at an angle $\theta$ with respect to the horizontal. What is the change in angular momentum of the projectile with respect to the launch point from the time it is launched to the time it reaches its maximum height?

A constant torque of $10 \text{ N} \cdot \text{m}$ is applied to a wheel for $5 \text{ seconds}$. What is the angular impulse on the wheel?

A figure skater is spinning with her arms extended. As she pulls her arms in, her moment of inertia decreases. According to the principle of conservation of angular momentum, what happens to her angular velocity?

A particle of mass $2 \text{ kg}$ is moving with a velocity of $3 \text{ m/s}$ along a line given by $y = 4 \text{ m}$ parallel to the x-axis. What is the magnitude of the angular momentum of the particle with respect to the origin?

A wheel initially at rest experiences an angular impulse of $20 \text{ kg} \cdot \text{m}^2/\text{s}$. If the moment of inertia of the wheel is $4 \text{ kg} \cdot \text{m}^2$, what is the final angular velocity of the wheel?