A point on the rim of a flywheel with radius $1.50 \mathrm{ft}$ has a linear velocity of $30.0 \mathrm{ft} / \mathrm{s}$. Calculate the time for it to complete $4 \pi \mathrm{rad}$

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.

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?

Satellite Dish A reflector for a satellite dish is parabolic in cross section, with the receiver at the focus $F$. The reflector is $1 \mathrm{ft}$ deep and $20 \mathrm{ft}$ wide from rim to rim (see the figure). How far is the receiver from the vertex of the parabolic reflector?

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 tangential acceleration? Provide a reason for your answer.

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?

Linear vs. Angular Speed A wheel of radius 30 centimeters revolves at a rate of 10 revolutions per second. A dot is painted at a point $P$ on the rim of the wheel (see figure).

Find $d x / d t$ as a function of $\theta$.

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?

Viewed from above, a turntable rotates counterclockwise. The angular velocity vector is then (a) tangential to the turntable's rim, (b) out of the plane of the turntable, (c) counterclockwise, (d) none of the preceding.

The water side of the wall of a $100$-$\mathrm{m}$-long dam is a quarter circle with a radius of $10 \mathrm{~m}$. Find the hydrostatic force on the dam and its line of action when the dam is filled to the rim.

Eight-year-old Allie Oop, an aspiring basketball player, shoots five feet from the hoop. She is trying to get the ball above the rim, which is set at a height of 10 feet. She releases the ball from an initial height of 4 feet. The following equation models the path of the ball, where x is the horizontal distance in feet that the ball has traveled and h is the ball's height in feet above the ground.

$$h=-0.4 x^2+3 x+4$$

Allie practices her shot, but it never reaches the rim, so her father lowers the hoop to 9 feet. Now will the ball reach the height of the rim? Justify your answer.

Suppose a bicycle wheel is rotated about an axis through its rim and parallel to its axle. Choose the best explanation from among the following: I. The moment of inertia is greatest when an object is rotated about its center. II. The mass and shape of the wheel remain the same. III. Mass is farther from the axis when the wheel is rotated about the 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.

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