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

I = (2/5)mr² = (2/5) * 8200kg * (0.9m)² = 2657 kg·m²
= I
70N * 0.9m = 2657kg·m² *
= 0.0237 rad/s²

= ½t²
2 rads = ½ * 0.0237rad/s² * t²
t = 23.026 s

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