Thursday
March 23, 2017

Post a New Question

Posted by 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 - , 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

First Name:
School Subject:
Answer:

Related Questions

More Related Questions

Post a New Question