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?).

A wheel with a 30-cm radius is rotating at a rate of 3 radians/sec. What is the linear speed of a point on its rim, in meters per minute?

A wheel of radius $27.0 \mathrm{~cm}$ has an angular speed of $47.0 \mathrm{rpm}$. Calculate the linear speed (in $\mathrm{m} / \mathrm{s}$ ) of a point on its rim.

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 $t = 2.0 \text{~s}$.

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 $t = 4.0 \text{~s}$.

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?

A 60.0-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 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 m/s relative to Earth. How much work does the woman do to set herself and the turntable into motion?

Solve. Give answers to two significant digits. A merry-go-round 40 ft in diameter makes four revolutions every minute. What is the speed of a seat on the rim?

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 $60.0-\mathrm{kg}$ 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?

The dial of a standard clock has a 10 -centimeter radius. One end of an elastic string is attached to the rim at 12 and the other to the tip of the 10-centimeter minute hand. At what rate is the string stretching at 12:15 (assuming that the clock is not slowed down by this stretching)?

A beetle sits near the rim of a turntable that rotates without friction about a vertical axis. The beetle then begins to walk toward the center of the turntable. As a result, does the angular speed of the turntable increase, decrease, or stay the same?

In each of the following sentences, underline the subject once and the predicate twice. Part of the caldera around Vesuvius, known as the Somma Rim, was formed approximately 17,000 years ago.

A 50.0-kg child stands at the rim of a merry-go-round of radius 2.00 m, rotating with an angular speed of 3.00 rad/s. What is the minimum force between her feet and the floor of the carousel that is required to keep her in the circular path?