Posted by **saud** on Monday, December 5, 2011 at 11:59pm.

A uniform solid cylinder of radius R and a thin uniform spherical shell of radius R both roll without slipping. If both objects have the same mass and the same kinetic energy, what is the ratio of the linear speed of the cylinder to the linear speed of the spherical shell?

- physics -
**drwls**, Tuesday, December 6, 2011 at 1:10am
K.E. = Etranslational + Erotational

For either cylinder or sphere, V = R*w

For a uniform solid sphere:

K.E. = (1/2)MV^2 + (1/2)I w^2

= (1/2)MV^2 + (1/2)*(2/5)M*R^2*(V/R)^2

= (7/10) M V^2

For a uniform solid cylinder:

K.E. = (1/2)MV^2 + (1/2)((1/2)MR^2*(V/w)^2

= (3/4)M V^2

If masses are equal, AND KE's are equal,

V(cylinder)^2/V(sphere)^2 = (4/3)/(10/7)

= 0.93333

V(cylinder)/V(sphere) = 0.9661

## Answer This Question

## Related Questions

- Physics - Four objects - a hoop, a solid cylinder, a solid sphere, and a thin, ...
- physics - Consider two solid uniform cylinders that have the same mass and ...
- Physics - A sphere of radius 2.84 cm and a cylinder of radius 8.97 cm are ...
- physics - A solid uniform cylinder of mass 4.6 kg and radius 0.051 m rolls ...
- Physics - A cylinder (I = 1/2 MR2), a sphere (I = 2/5MR2), and a hoop (I = MR2...
- Physics - A cylinder ( I = 1/2 MR2), a sphere ( I = 2/5 MR2), and a hoop ( I = ...
- Physics - A 190 g basketball has a 37.3 cm diameter and may be approximated as a...
- physics - A 15.0 kg mass and a 10.0 kg mass are suspended by a pulley that has a...
- physics - A uniform solid cylinder of mass 1kg roll with out slipping on aflat ...
- INTRO TO PHYSICS - Each of the following objects has a radius of 0.174 m and a ...

More Related Questions