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

increasing transnational kinetic energy. because the transnational kinetic energy formula consists of only two variables, mass and velocity, increasing one of those properties is the only way to increase an object's transnational kinetic energy. increases to mass and velocity, however, do not have the same impact.

hypothesising or postulating