A $60.0-\mathrm{kg}$ woman stands at the rim of a horizontal turntable having a moment of inertia of $500 \mathrm{~kg} \cdot \mathrm{m}^2$ and a radius of $2.00 \mathrm{~m}$. The turntable is initially at rest and is free to rotate about a frictionless, vertical axle through its center. The woman then starts walking around the rim clockwise (as viewed from above the system) at a constant speed of $1.50 \mathrm{~m} / \mathrm{s}$ relative to the Earth. (b) How much work does the woman do to set herself and the turntable into motion?

A $60.0-\mathrm{kg}$ woman stands at the rim of a horizontal turntable having a moment of inertia of $500 \mathrm{~kg} \cdot \mathrm{m}^2$ and a radius of $2.00 \mathrm{~m}$. The turntable is initially at rest and is free to rotate about a frictionless, vertical axle through its center. The woman then starts walking around the rim clockwise (as viewed from above the system) at a constant speed of $1.50 \mathrm{~m} / \mathrm{s}$ relative to the Earth. (a) In what direction and with what angular speed does the turntable rotate?

At $t=3.00$ s a point on the rim of a $0.200$-m-radius wheel has a tangential speed of $50.0$ m$/$s as the wheel slows down with a tangential acceleration of constant magnitude $10.0$ m$/$s$^2$. (b) Calculate the angular velocities at $t=3.00$ s and $t=0$.

Solve the given problems.

Find the equation describing the rim of a circular porthole $2$ ft in diameter if the top is $6$ ft below the surface of the water. Take the origin at the water surface directly above the center of the porthole.

A wheel of radius 30 cm is rotating at a rate of 2.0 revolutions every 0.080 s. (a) Through what angle, in radians, does the wheel rotate in 1.0 s? (b) What is the linear speed of a point on the wheel's rim? (c) What is the wheel's frequency of rotation?

The angular position of a point on the rim of a rotating wheel is given by $\theta = 4.0t - 3.0t^2 + t^3$, where $\theta$ is in radians and t is in seconds. What are the angular velocities at $t = 4.0 \text{~s}$.

A dart is thrown horizontally with an initial speed of 10 m/s toward point P, the bull's-eye on a dart board. It hits at point Q on the rim, vertically below $P, 0.19$ s later. What is the distance $P Q$ ?

A uniform sphere with mass $28.0 \mathrm{~kg}$ and radius $0.380 \mathrm{~m}$ is rotating at constant angular velocity about a stationary axis that lies along a diameter of the sphere. If the kinetic energy of the sphere is $176 \mathrm{~J}$, what is the tangential velocity of a point on the rim of the sphere?

Estimate the moment of inertia of a bicycle wheel $67 \mathrm{~cm}$ in diameter. The rim and tire have a combined mass of $1.1 \mathrm{~kg}$. The mass of the hub (at the center) can be ignored (why?).

The angular position of a point on the rim of a rotating wheel is given by $\theta = 4.0t - 3.0t^2 + t^3$, where $\theta$ is in radians and t is in seconds. What are the angular velocities at $t = 2.0 \text{~s}$.

An electric turntable $0.750$ m in diameter is rotating about a fixed axis with an initial angular velocity of $0.250$ rev$/$s and a constant angular acceleration of $0.900$ rev$/$s$^2$.
($c$) What is the tangential speed of a point on the rim of the turn- table at $t=0.200$ s?

The angular position of a point on the rim of a rotating wheel is given by $\theta = 4.0t - 3.0t^2 + t^3$, where $\theta$ is in radians and t is in seconds. What is the instantaneous angular acceleration at the end of this time interval?

A carousel with a 50 -foot diameter makes 4 revolutions per minute. (a) Find the angular speed of the carousel in radians per minute. (b) Find the linear speed of the platform rim of the carousel.

When the string is pulled with a force $p$ tangent to the rim, it gives the cylinder an angular acceleration $\alpha$, if the cylinder had fourfold the radius but everything else was the same the angular acceleration would be?