# Physics

Equate the increase in potential energy at the higher elevation, M g H, to the decrease in kinetic energy. Make sure you include the kinetic energy of rotation, which is (1/2) I w^2. For a sphere of radius R,
V = R w
and I =(2/5) I R^2
Therefore
KE(rotational) = (1/2)(2/5)M R^2(V/R)^2 = (1/5) M V^2
M g H = KE(translational) + KE(rotational)= (7/10)MV^2
V^2 = sqrt[(10/7)gH]

A bowling ball encounters a 0.76m vertical rise on the way back to the ball rack, as the drawing illustrates. Ignore frictional losses and assume that the mass of the ball is distributed uniformly. If the translational speed of the ball is 3.80m/s at the bottom of the rise, find the translational speed at the top.

Where does the translational speed at the bottom come in?

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1. A bicycle wheel has a diameter of 47.6 cm and a mass of 0.809 kg. The bicycle is placed on a stationary stand on rollers and a resistive force of 60.1 N is applied to the rim of the tire. Assume all the mass of the wheel is concentrated on the outside radius.
In order to give the wheel an acceleration of 3.18 rad/s2, what force must be applied by a chain passing over a sprocket with diameter 4.16 cm?

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