A wheel of radius $20.0 \mathrm{~cm}$ starts from rest and makes $6.00$ revolutions in $2.50 \mathrm{~s}$. (a) Find its angular velocity in rad/s. (b) Calculate its angular acceleration. (c) Calculate the final linear speed of a point on the rim of the wheel. (d) Calculate the linear acceleration of a point on the rim of the wheel.

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.

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.

The eyes of a basketball player are 6 feet above the floor. The player is at the free-throw line, which is 15 feet from the center of the basket rim (see the figure). What is the angle of elevation from the player’s eyes to the center of the rim? [Hint: The rim is 10 feet above the floor.]

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. $56.6 \times 2 \pi$

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 $1\frac{1}{4}''$ drywall screw is countersunk (i.e., screwed until it is below the surface of the drywall) by $\frac{1} {16}''$ to fasten a $\frac{5} {8}''$ sheet of drywall to the ceiling joist.
(a) How much of the screw extends into the joist?
(b) How much of the screw is within the drywall?

Two markers A and B on the same side of a canyon rim are 56 ft apart. A third marker C, located across the rim, is positioned so that ∠BAC = 72° and ∠ABC = 53°.. Find the distance between C and A.

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.

A wheel of radius 1.5 m rotates at a uniform speed. If a point on the rim of the wheel has a centripetal acceleration of $1.2\ m/s^2,$ what is the point's tangential speed?

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.

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.

Recreation Suppose that the ferris wheel of the Exercise earlier has a diameter of $220 \mathrm{ft}$. Determine the linear velocity of a car on the rim of the wheel.

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?