Question

A wheel is turning about an axis through its center with constant angular acceleration. Starting from...

A wheel is turning about an axis through its center with constant angular acceleration. Starting from rest, at t=0, the wheel turns through 8.00 revolutions in t= 12.5 s . At 12.5 s the kinetic energy of the wheel is 38.5 J .

1- For an axis through its center, what is the moment of inertia of the wheel?

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Answer #1

The angular acceleration of the wheel can be found out from kinematic formulae for rotational motion.

or

The wheel goes through revolutions, which is equal to

Substituting our values, we get

The angular velocity at the end of is

We know that rotational kinetic energy is

where is the moment of inertia for an axis through the center of rotation.

We rearrange the equation as

Substituting our values, we get

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