The formula for torque is:

We are given the length of the hammer (radius of the swing) and the torque produced. Using these values, we can solve for the force required.

We know that the work-kinetic energy theorem states that the work done is equal to the change of kinetic energy. In rotational terms this means that

In this case the initial angular velocity is .

We can convert our final angular velocity to radians per second.

We also can calculate the moment of inertia of the merry-go-round assuming that it is a uniform solid disk.

We can put this into our work equation now.

The centripetal force is what is acting on the rider. At the top of the Ferris wheel, the normal force is pointing up, and the gravitational force is pointing down. The sum of these two forces must equal the centripetal force pointing downward toward the center of the circle. Therefore the normal force must be smaller than the gravitational force. At the bottom of the Ferris wheel, the same forces are present. However, the sum of these forces must equal the centripetal force point upward toward the center of the circle. Therefore the normal force must be greater than the gravitational force. Since the normal force must be greater than the gravitational force at the bottom and less than the gravitational force at the top, the force at the bottom must be greater than the force on the top.

Torque is a force times the radius of the circle, given by the formula:

In this case, we are given the radius in centimeters, so be sure to convert to meters:

Use this radius and the given force to solve for the torque.

Torque is a force times the radius of the circle, given by the formula:

In this case, we are given the radius in centimeters, so be sure to convert to meters:

Use this radius and the given force to solve for the torque.

We know that the work-kinetic energy theorem states that the work done is equal to the change of kinetic energy. In rotational terms this means that

In this case the initial angular velocity is .

We can convert our final angular velocity to radians per second.

We also can calculate the moment of inertia of the merry-go-round assuming that it is a uniform solid disk.

We can put this into our work equation now.

The centripetal force is what is acting on the rider. At the top of the Ferris wheel, the normal force is pointing up, and the gravitational force is pointing down. The sum of these two forces must equal the centripetal force pointing downward toward the center of the circle. Therefore the normal force must be smaller than the gravitational force. At the bottom of the Ferris wheel, the same forces are present. However, the sum of these forces must equal the centripetal force point upward toward the center of the circle. Therefore the normal force must be greater than the gravitational force. Since the normal force must be greater than the gravitational force at the bottom and less than the gravitational force at the top, the force at the bottom must be greater than the force on the top.

The given equation for moment of inertia is:

Use the given values for the mass and radius of the ball to solve for the moment of inertia.

We know that the work-kinetic energy theorem states that the work done is equal to the change of kinetic energy. In rotational terms this means that

In this case the initial angular velocity is .

We can convert our final angular velocity to radians per second.

We also can calculate the moment of inertia of the merry-go-round assuming that it is a uniform solid disk.

We can put this into our work equation now.

Torque is a force times the radius of the circle, given by the formula:

In this case, we are given the radius in centimeters, so be sure to convert to meters:

Use this radius and the given force to solve for the torque.