A thin uniform bar has two small balls glued to its ends. The bar is $2.00 \mathrm{~m}$ long and has mass $4.00 \mathrm{~kg}$, while the balls each have mass $0.500 \mathrm{~kg}$ and can be treated as point masses. Find the moment of inertia of this combination about each of the following axes:
(a) an axis perpendicular to the bar through its center;
(b) an axis perpendicular to the bar through one of the balls;
(c) an axis parallels to the bar through both balls.

A uniform bar has two small balls glued to its ends. The bar is $2.00 \mathrm{~m}$ long and has mass $4.00 \mathrm{~kg}$, while the balls each have mass $0.500 \mathrm{~kg}$ and can be treated as point masses. Find the moment of inertia of this combination for the axis perpendicular to the bar through its center.

A thin, uniform, 3.80-kg bar, 80.0 cm long, has very small 2.50-kg balls glued on at either end. It is supported horizontally by a thin, horizontal, frictionless axle passing through its center and perpendicular to the bar. Suddenly the right-hand ball becomes detached and falls off, but the other ball remains glued to the bar. Find the angular velocity of the bar just as it swings through its vertical position.

A twirler's baton is made of a slender metal cylinder of mass $M$ and length $L$. Each end has a rubber cap of mass $m$, and you can accurately treat each cap as a particle in this problem. Find the total moment of inertia of the baton about the usual twirling axis (perpendicular to the baton through its center).

A twirler's baton is made of a slender metal cylinder of mass $M$ and length $L$. Each end has a rubber cap of mass $m$ and you can accurately treat each cap as a particle in this problem. Find the total moment of inertia of the baton about the usual twirling axis (perpendicular to the baton through its center).

A grindstone in the shape of a solid disk with diameter 0.520 m and a mass of 50.0 kg is rotating at 850 rev/min. You press an ax against the rim with a normal force of 160 N, and the grindstone comes to rest in 7.50 s. Find the coefficient of friction between the ax and the grindstone. You can ignore friction in the bearings.

Ultracentrifuge. Find the required angular speed (in rpm) of an ultracentrifuge for the radial acceleration of a point $2.50 \mathrm{~cm}$ from the axis to equal $400,000 \mathrm{~g}$.

An electric turntable $0.750$ m in diameter is rotating about a fixed axis with an initial angular velocity of $0.250$ rev$/$s and a constant angular acceleration of $0.900$ rev$/$s$^2$.
(d) What is the magnitude of the $\it{resultant}$ acceleration of a point on the rim at $t=0.200$ s?

An electric turntable $0.750$ m in diameter is rotating about a fixed axis with an initial angular velocity of $0.250$ rev$/$s and a constant angular acceleration of $0.900$ rev$/$s$^2$.
($c$) What is the tangential speed of a point on the rim of the turn- table at $t=0.200$ s?

Exercise! An exercise bike that you pedal in place has a bicycle chain connecting the wheel you pedal to the large wheel in front. For the wheel diameters shown, how many rpm must you produce to turn the large wheel at $75 \mathrm{rpm}$?

An electric turntable $0.750$ m in diameter is rotating about a fixed axis with an initial angular velocity of $0.250$ rev$/$s and a constant angular acceleration of $0.900$ rev$/$s$^2$.
(b) Through how many revolutions has the turntable spun in this time interval?

You are designing a centrifuge to spin at a rate of 15,000 rev/min.

$(b)$ It takes 1 min, 15 s for the centrifuge to spin up to its maximum rate of revolution from rest. Calculate the magnitude of the tangential acceleration of the centrifuge while it is spinning up, assuming that the tangential acceleration is constant.

Spin cycles of washing machines remove water from clothes by producing a large radial acceleration at the rim of the cylindrical tub that holds the water and clothes. Estimate the diameter of the tub in a typical home washing machine. What is the rotation rate, in rev/min, of the tub during the spin cycle if the radial acceleration of points on the tub wall is 3g?

DVDs. The angular speed of digital video discs (DVDs) varies with whether the inner or outer part of the disc is being read. (CDs function in the same way.) Over a $133 \mathrm{~min}$ playing time, the angular speed varies from $570 \mathrm{rpm}$ to $1600 \mathrm{rpm}$. Assuming it to be constant, what is the angular acceleration (in $\mathrm{rad} / \mathrm{s}^2$ ) of such a DVD?