Time to Rotate Metal Sphere 1 Time

[atomB]

Homework Statement

A girl pushes 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 = 45N and that the pressured water provides a frictionless support. How long will it take her to rotate the sphere one time, starting from rest?

m = 8200kg
r = 90cm = 0.90m
F_applied = 45N

Homework Equations

τ = RF_perpendicular
α = τ/I
I = 2/5MR²
θ = ω₀t + 1/2αt²
θ = 2∏r

The Attempt at a Solution

Solve for τ = (45N)(0.90m) = 40.5 N*m
Solve for α = 40.5N*m/[2/5(8200kg)(0.90m)²] = 0.01524 rad/s²
Solve for θ = 2∏(0.90m) = 5.65486 rad

Solve for t: 5.65486 rad = 0 + 1/2(0.01524 rad/s²)(t²)
t = 27.24 s

The answer isn't right when I submitted it; I thought my process was correct. Where did I go wrong here?

Thanks!

 

[Orodruin]

Solve for θ = 2∏(0.90m) = 5.65486 rad

The angle θ does not depend on the radius. A full turn is always 2pi radians.

 

[atomB]

You're absolutely right; for some reason, I was thinking circumference. Thanks for catching that!