Question

There is a girl pushing on a large stone sphere. The sphere has a mass of 8200 kgand 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 = 30N and that the pressured water provides a frictionless support.1) How long will it take her to rotate the sphere one time, starting from rest?

Answer 1

Answer:

t = 35.16 s

Explanation:

Inertia  

I = (2/5)*m*r²

I = (2/5) * 8200 kg * (0.9m)²

I = 2657 kg·m²

τ = I*α

30N * 0.9m = 2657kg·m² * α

α = 0.01016 rad/s²

Θ = ½α*t²

2π rads = ½ * 0.01016rad/s² * t²

t =sqrt(4π rads/0.0106rad/s²)

t = 35.16 s