A solid sphere has a mass M and radius R resting at an incline with height H. Ca

Question

A solid sphere has a mass M and radius R resting at an incline with height H. Calculate the translational speed of the center of mass at the bottom of the incline if the sphere rolling down without slipping (the moment inertia of the solid sphere about it center mass is I) - please see image

A solid sphere has a mass M and radius of R resting at an incline with height H. Calculate the translational speed of the center of mass at the bottom of the incline if the sphere rolling down without slipping (the moment inertia of the solid sphere about it enter mass is I). A horizontal platform in the shape of a circular disc rotates freely in a horizontal plane about a frictionless vertical axis as in the figure. The platform has a mass M = 200 km and radius R = 4 m. Student whose mass is m = 100 kg walks slowly from the rim of the disc toward its center. If the angular speed of the system is 4 rad/s when the student is at the rim, what is the angular speed when she reaches a point r = 1 m from the center? (The moment inertia of the circular disc is given to be I = 1/2 MR2).

Explanation / Answer

Ei = Ef

M g H = 1/2 mv^2 + 1/2 I w^2

w = v/R

M g H = 1/2 M V^2 1/2 I/R^2 v^2

v = sqrt( 2 M g H/( M V^2 + I/R^2))

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