A hollow, spherical shell with a mass of $2.00 \textrm{ kg}$ rolls without slipping down a $38.0 ^ { \circ }$slope.

(a) Find the acceleration, the friction force, and the minimum coefficient of friction needed to prevent slipping.

(b) How would your answers to part (a) change if the mass were doubled to $4.00 \textrm{ kg}$?

A hollow spherical shell with a mass of $65\text{ kg}$ rolls without slipping down a slope that makes an angle of $31^{\circ}$ with the horizontal plane. Find the magnitude of the acceleration $a_{cm}$ of the center of mass of the spherical shell. Take the free-fall acceleration to be $g=9.80\text{ m/s}^2$.

A lawn roller in the form of a thin-walled, hollow cylinder with mass M is pulled horizontally with a constant horizontal force F applied by a handle attached to the axle. If it rolls without slipping, find the acceleration and the friction force.

A woman with mass 50 kg is standing on the rim of a large disk that is rotating at 0.80 rev/s about an axis through its center. The disk has mass 110 kg and radius 4.0 m. Calculate the magnitude of the total angular momentum of the woman–disk system. (Assume that you can treat the woman as a point.)

An AISI 304 stainless steel sheet is going through an annealing process inside an electrically heated oven, The ambient air inside the oven is $600^\circ C,$ while the surrounding surfaces of the oven are at a uniform temperature of $750^\circ C.$ If the emissivity of the stainless steel sheet is 0.40 and the average convection heat transfer coefficient is $10W/m^2 \cdot K,$ determine the temperature of the stainless steel sheet.

A uniform thin spherical shell has a radius of $2.00 \text{~m}$ and a mass of $300 \text{~kg}$ and its center is located at the origin of a coordinate system. Another uniform thin spherical shell with a radius of $1.00 \text{~m}$ and a mass of $150 \text{~kg}$ is inside the larger shell, with its center at $0.600 \text{~m}$ on the $x$ axis. What is the gravitational force of attraction between the two shells?

On the basis of the information, calculate the ultimate tensile strength (engineering) of 304 stainless steel.

The Capital account balance minus the net loss minus the Drawing account balance equals a. net loss. b. total liabilities. c. the capital amount shown on a balance sheet. d. the capital amount shown on an income statement.

A string is wrapped several times around the rim of a small hoop with radius 8.00 cm and mass 0.180 kg. The free end of the string is held in place and the hoop is released from rest. After the hoop has descended 75.0 cm, calculate the angular speed of the rotating hoop.

An Unfair Race This applet shows the results of releasing a frictionless block and a rolling disk with equal masses from the top of identical inclined planes. Which of the following is the best explanation of the results shown in the applet?

A) The disk loses energy to friction as it rolls, but the box is frictionless and so it speeds up more quickly and gets to the bottom first.

B) The potential energy of the disk is converted into translational and rotational kinetic energy, so the translational speed grows more slowly than that of the box, which has no rotational energy.

C) The net forces on the two objects are equal, but the force on the disk gets partially used up in creating the torque necessary to make it roll.

D) The net forces on the two objects are equal, but the force on the disk is not directed parallel to the ramp, and so does not create as great an acceleration down the ramp.

A hollow spherical shell has mass 8.20 kg and radius 0.220 m. It is initially at rest and then rotates about a stationary axis that lies along a diameter with a constant acceleration of $0.890 \mathrm{rad} / \mathrm{s}^{2}$. What is the kinetic energy of the shell after it has turned through 6.00 rev?

Three forces are applied to a wheel of radius 0.350, as shown in the figure (Intro 1figure). One force is perpendicular to the rim, one is tangent to it, and the other one makes a 40.0 angle with the radius. Assume that $F_1=12.4~\text{N}$, $F_2=14.2~\text{N}$, and $F_3=8.75~\text{N}$.

Part A What is the magnitude of the net torque on the wheel due to these three forces for an axis perpendicular to the wheel and passing through its center?

Part B What is the direction of the net torque in part (A), into the page or out of the page?

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.

What fraction of the total kinetic energy is rotational for the following objects rolling without slipping on a horizontal surface?
(b) a uniform sphere;