In Example 10.5 (Section 10.3) we found that for a hollow cylindrical shell rolling without slipping on a horizontal surface, half of the total kinetic energy is translational and half is rotational. What fraction of the total kinetic energy is rotational for the following objects rolling without slipping on a horizontal surface?
(a) A uniform solid cylinder.
(b) A uniform sphere.
(c) A thin-walled hollow sphere.
(d) A hollow, cylinder of outer radius R and inner radius R/2.
*I thought I was looking right at the chart the question was talking about but I still am getting wrong answers!!!
2007-11-07 09:27:26 · 1 answers · asked by Walachka 3 in Science & Mathematics ➔ Physics
The rotational kinetic energy is 1/2 I ω²
Where I is the moment of inertia and ω is the angular velocity.
Linear kinetic energy is 1/2 m v²
The linear speed of the object is the same as the speed of a point on the edge of the rotating shape. If they didn't have the same speed, there would be slipping. You can use this relationship to write ω in terms of v.
For each of your shapes you need to find I. Most, if not all, will probably be listed in your textbook.
Substitute for I and ω in the equation for rotational KE. Divide rotational KE by linear KE to get the ratio of rotational KE to linear KE.
2007-11-07 09:43:40 · answer #1 · answered by Demiurge42 7 · 0⤊ 2⤋