A uniform sphere with mass 23.0 kg and radius 0.330 m is rotating at constant angular velocity about a stationary axis that lies along a diameter of the sphere. Part A If the kinetic energy of the sphere is 238 J, what is the tangential velocity of a point on the rim of the sphere?

v = 156.78 m/s

Explanation:

To find the tangential velocity of a point on a rim of the sphere, you use the following formula for the kinetic energy of the sphere:

   (1)

K: kinetic energy = 238 J

I: moment of inertia of the sphere

w: angular velocity of the sphere

Furthermore, you take into account the following equation for the moment of inertia of a sphere (with an axis crossing a diameter), and also the following equation for the angular speed:

    (2)

M: mass of the sphere  = 23.0 kg

R: radius of the sphere = 0.330 m

      (3)

v: tangential velocity of a point on the rim of the sphere

You replace the equation (2) and (3) into the equation (1):

You solve the previous equation for v, and then replace the values of the parameters:

The tangential velocity  of a point on the rim is 156.78 m/s

568.98

explanation:

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