# Rolling motion of a rigid body problem

#### Minchi

1. A solid sphere has a radius of 0.200 m and a mass of 150 kg. How much work is required to get the sphere rolling with an angular speed of 50.0 rad/s on a horizontal surface? Assume the sphere starts from rest and rolls without slipping

2. The attempt at a solution

I found V first.

V= rw
= 0.2 x 50
=10 m/s

Then Fc

Fc = mv^2/r
= (150)(10)^2 / 0.2
=75000 N

W= F X R
= 75000 x 0.2
= 15000 J

The answer the teacher gave was 1.05 x 10^4 J or 10500 J...

What did I do wrong?

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#### HallsofIvy

Homework Helper
1. A solid sphere has a radius of 0.200 m and a mass of 150 kg. How much work is required to get the sphere rolling with an angular speed of 50.0 rad/s on a horizontal surface? Assume the sphere starts from rest and rolls without slipping

2. The attempt at a solution

I found V first.

V= rw
= 0.2 x 50
=10 m/s

Then Fc

Fc = mv^2/r
= (150)(10)^2 / 0.2
=75000 N

W= F X R
= 75000 x 0.2
= 15000 J
This is the rotational energy. In addition to just spinning in place the sphere is moving forward. You have to take the translational kinetic energy into account too.

The answer the teacher gave was 1.05 x 10^4 J or 10500 J...

What did I do wrong?

#### Minchi

I = mi ri^2
=(150)(0.2)^2
= 6 kg m2

KE= 1/2 I w^2
=(0.5)(6)(50)^2
=7500 J

um...where do I fit this into what I did above?

Was all my steps above required to the question?

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