Rotational Kinetics

Rotational motion has two requirements: all particles must move about a fixed axis, and move in a circular path. Since the path of most planets is not circular, they do not exhibit rotational motion.

Recall that = . We can assume that the angular velocity is constant, so we can use this equation to solve our problem. Each revolution corresponds to an angular displacement of 2Π radians. Thus 100 revolutions corresponds to 200Π radians. Thus:

Again, we can assume that the acceleration is constant, and use the following equation:

We know that = . Since we want to solve for the total angular displacement, or φ , we rearrange this equation:

However, we are asked for the number of revolutions, not the number of radians. Since there are 2Π radians in every revolution, we divide our number by 2Π :

Thus the merry-go-round revolves about 4 times in that period.