A pebble is dropped into a water well, and the splash is heard $16 \mathrm{~s}$ later, as illustrated in the cartoon strip. Estimate the distance from the rim of the well to the water's surface.

A waterwheel with diameter 12 ft turns at 0.3 rad/s}.

The waterwheel is connected by an axle to a grindstone with diameter 3 ft. What is the angular velocity of points on the rim of the grindstone?

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?

A potter's wheel with radius 8 in. spins at 150 rpm. Find the angular and linear speeds of a point on the rim of the wheel.

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.

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.

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?

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?

A standard basketball rim has a circumference of about 56.6 inches. Which expression can be used to find the diameter of the rim? A. $\frac{56.6}{2 \pi}$ B. $56.6 \times \pi$ C. $\frac{56.6}{\pi}$ D. $56.6 \times 2 \pi$

Two points are located on a rigid wheel that is rotating with an increasing angular velocity about a fixed axis. The axis is perpendicular to the wheel at its center. Point 1 is located on the rim, and point 2 is halfway between the rim and the axis. At any given instant, which point (if either) has the greater angular acceleration? Provide a reason for your answer.

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

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 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 child’s centripetal acceleration?

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 beginning of this time interval?