Posted by **Kristen** on Sunday, January 27, 2008 at 5:18pm.

A uniform spherical shell of mass M and radius R rotates about a vertical axiss on frictionless bearings. A massless cord passes around the equator of the shell, over a pulley of rotational inertia I and radius r, and is attached to a small object mass m. There's not friction on teh pulleys axle; the cord doesnt slip on teh pulley. Whats the speed of the object after it falls a distance h from rest? Use energy considerations (g=gravity, M=mass M, R=radius R, I=inertia I, r=radius r, and m=mass m)

- AP Physics -
**drwls**, Sunday, January 27, 2008 at 6:19pm
After falling a distance h, Potential energy m g h is converted to kinetic energy of the rotating shell, the falling mass, and the pulley. Let V be the velcoity of the mass at time t.

The angular velocity of the shell is ws= V/R and its moment of inertia is

Is = (2/3)MR^2

The moment of inertia of the pulley is I, its angular velocity is wp = V/r, and its radius is r.

mgh = (1/2)mV^2 + (1/2)(2/3)MR^2*(V/R)^2 + (1/2) I (V/r)^2

= V^2 [(1/2)m + (1/3)M + (1/2)I/r^2]

V^2 = 2gh/[1 + (2/3)M/m + I/(mr^2)]

## Answer this Question

## Related Questions

AP physics - A uniform spherical shell of mass M and radius R rotates about a ...

Physics - A uniform spherical shell of mass M = 19.7 kg and radius R = 1.62 m ...

physics - A uniform spherical shell of mass M = 8.00 kg and radius R = 0.550 m ...

Physics - A particle with a charge of -60.0 nC is placed at the center of a ...

Physics - Note: The left-hand mass is equal to the sum of the other two masses. ...

Physics gravity - A thin spherical shell has a radius of 2.4 m and a mass of 410...

physics - A block of mass 4.44 kg lies on a frictionless horizontal surface. The...

Physics - A disk and a hollow spherical shell, like a basketball, are released ...

physics - A system has three masses, a 10kg mass is lying on a level surface and...

physics - A block (mass = 2.9 kg) is hanging from a massless cord that is ...