The photograph below shows a girl pushing on a large stone sphere. The sphere ha

Question

The photograph below shows a girl pushing on a large stone sphere. The sphere has a mass of 8200 kg and a radius of 90 cm and floats with nearly zero friction on a thin layer of pressurized water. Suppose that she pushes on the sphere tangent to its surface with a steady force of F = 70 N and that the pressured water provides a frictionless support. How long will it take her to rotate the sphere one time, starting from rest? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Moment of inertia I = 2/5 mR^2

I = 2/5 * 8200 * 0.9* 0.9

I = 2656.8 kgm^2

for torque T = I Alpha = F x d

Alpha = angular accleration = 7* 0.9/(2656.8)

alpha = 0.0237 rad/s^2

angular dispalcement theta = 0.5 at^2

theta = 2pi rad here

so

t^2 = 2 * 2*3.14/(0.0237)

t = 23.03 secs

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