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Rotational Kinetic Energy

Conservation of Kinetic Energy

         

A solid ball rolls on a slope from rest starting from a height of \(H=7.0\text{ m}\) and then rolls on a horizontal region, as shown in the above figure. The horizontal distance of the slope and the distance of the horizontal region are both equal to \(L=6 \text{ m},\) and the height of the horizontal region is \(h=3.0\text{ m}.\) Approximately how far horizontally from point \(P\) does the ball hit the floor?

The rotational inertia of a solid sphere about any diameter is \(I=\frac{2}{5}MR^2,\) where \(M\) and \(R\) are the mass and the radius of the solid sphere, respectively, and the gravitational acceleration is \(g=9.8\text{ m/s}^2.\)

A brand new off-road \(6 \times 6\) pickup truck has six wheels. If the total mass of the pickup truck is \(1200\text{ kg}\) and the mass of each of the six wheels is \(19\text{ kg},\) what fraction of its total kinetic energy is due to the rotation of the wheels about their center axles?

Assume that each of the six wheels is a uniform disk.

A very thin hoop with a mass of \(180\text{ kg}\) is rolling along a horizontal floor. If the speed of the hoop's center of mass is \(0.180\text{ m/s},\) how much work must be done on the hoop to stop it?

A solid cylinder with radius \(40\text{ cm}\) and mass \(12\text{ kg}\) is rolling down from rest without slipping for a distance of \(L=10.0\text{ m},\) as shown in the above figure. The angle of the slope is \(\theta=30^\circ.\) What is the approximate angular speed of the cylinder about its center when it just meets the bottom of the slope, assuming that the gravitational acceleration is \(g=9.8\text{ m/s}^2?\)

Consider a situation where a uniform solid sphere, which was rolling smoothly along a horizontal floor, rises up along a \(30.0^\circ\) slope. If it stops after it has rolled \(9.00\text{ m}\) along the slope and then begins to roll backward, what was its initial speed?

The rotational inertia of a solid sphere about any diameter is \(I=\frac{2}{5}MR^2,\) where \(M\) and \(R\) are the mass and the radius of the solid sphere, respectively, and the gravitational acceleration is \(g=9.8\text{ m/s}^2.\)

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