• Support PF! Buy your school textbooks, materials and every day products Here!

Ratio of translational velocity to rotational velocity.

  • #1
1. A ball of mass m and radius R is both sliding and spinning on a horizontal surface so
that its rotational kinetic energy equals its translational kinetic energy.What is the ratio of the ball’s center-of-mass speed to the speed due to rotation only of a point on the ball’s surface? The moment of inertia of the ball is 0.56mR2 .

(For ease, I will refer to omega as w from here on out)

Homework Equations



KE = .5(I)(w)2 = .5mv2

The Attempt at a Solution



So if I understand it correctly the problem basically wants the ratio of linear velocity to rotational velocity, v to w. So, I set .5Iw2 = 1/2mv2

From here, I plugged in the given moment of inertia of the ball.

.5(.56mR2)(w)2 = .5mv2

Then I cancelled out the .5 and the m,

.56R2w2 = v2

Square rooted both sides,

sqrt(.56)Rw = v

but from here I am unsure of how I could possibly eliminate the R, and this causes big problems when finding a ratio. Any suggestions? Did I go wrong somewhere prior to this point? If I could just get that R, it should be easy I would think, but its a variable...
 

Answers and Replies

  • #2
kuruman
Science Advisor
Homework Helper
Insights Author
Gold Member
8,933
2,340
Read the problem carefully. You are looking for the ratio of the speed of the center of mass to the speed of a point on the surface of the sphere. The latter quantity is not ω; it is a linear speed (in m/s) so the final answer must be a dimensionless quantity.
 

Related Threads on Ratio of translational velocity to rotational velocity.

Replies
4
Views
3K
  • Last Post
Replies
5
Views
5K
  • Last Post
Replies
2
Views
5K
  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
19
Views
17K
  • Last Post
Replies
1
Views
321
  • Last Post
Replies
3
Views
1K
Top