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.

Nineteen items on the rim of a circle of radius 1 are to be chosen. Show that, for any choice of these points, there will be an arc of (arc) length 1 that contains at least 4 of them.

A bicycle rim has a diameter of 0.65 m and a moment of inertia, measured about its center, of $0.19 \mathrm { kg } \cdot \mathrm { m } ^ { 2 }$. What is the mass of the rim?

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.

Fill in each blank so that the resulting statement is true. The multiplicative identity matrix of order 3 is $I_{3}=$____

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 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.

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.]

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.

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 the two canyon rims. (Assume they are parallel.)

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

During the 2014 Olympic games, snowboarder Shaun White rose $6.4 \mathrm{~m}$ vertically above the rim of the half-pipe. With what speed did he launch from the 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?

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.