# Finding Rotational Kinetic Energy of Sphere on Ramp

## Homework Statement

If Inga, the Laboratory Assistant, rolls a spare head down a 4 m ramp because it was spherical and solid and too heavy at 4.5 kg at a speed of 4.5 m/s, what was its total kinetic energy?

KE = (1/2) I ω^2
I = (2/5) MR^2

## The Attempt at a Solution

Basically, I'm not sure how to solve this without the sphere's radius. Any help, solutions, or hints would be highly appreciated.

haruspex
Homework Helper
Gold Member
2020 Award
Just go ahead with the algebra and you should find the radius cancels out. The rotational KE of a sphere is in fixed ratio to its linear KE, regardless of radius.

So does this look correct:

KE = (1/2)(4.5 kg)(4.5m/s)^2 + (1/2)(2/5)(4.5)r^2[(4.5m/s)/r]^2
KE = 6.75 J + 18.225 J
KE = 24.98 J

Where'd that 6.75 J come from?

Where'd that 6.75 J come from?
Hmm..I too am now wondering the same.

Is this better:

KE = 45.453 J + 18.225 J
KE = 63.69 J

haruspex
Homework Helper
Gold Member
2020 Award
Hmm..I too am now wondering the same.

Is this better:

KE = 45.453 J + 18.225 J
KE = 63.69 J
Still a bit low. I get 45.56+18.23=63.79

Still a bit low. I get 45.56+18.23=63.79

That's also what I'm getting. Joel, I think you're not plugging into your calculator correctly.