For this problem, consider the kinetic energy of a rolling wheel on level ground

Question

For this problem, consider the kinetic energy of a rolling wheel on level ground. (a) Suppose the wheel is a hoop of radius r and mass m, rolling at speed upsilon. If the wheel is rolling on level ground, what is the relationship between its angular velocity around its center and the speed of its center along the ground? (b) The total kinetic energy of the wheel is the sum of the kinetic energy due to the motion of the center of mass 1/2mupsilon^2 and the kinetic energy due to motion around the center of mass. Write an expression for the total kinetic energy of the rolling wheel.

Explanation / Answer

Here ,

a) as the wheel is rolling on the ground

angular speed = v/r

b)

for the total kinetic energy = translational kinetic energy + rotational kinetic energy

total kinetic energy = 0.5 * m * v^2 + 0.5 *I * w^2

total kinetic energy = 0.5 *m * r^2 + 0.5 * m * r^2 * (v/r)^2

total kinetic energy = m * v^2

the total kinetic energy is m * v^2

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