Known

 which should be converted to meters ()

 which should be converted to 

We are dealing with circular motion so the first thing to do is to identify the force that is causing the centripetal motion.  In this case it is the force of friction which is holding the penny in place.  Therefore we know that the centripetal force is equal to the force of friction.

The centripetal force is equal to the mass times the centripetal acceleration.

To calculate the centripetal acceleration you will need to know the velocity of the penny and the radius that the penny sits at.

Therefore  

We also know that the frictional force is related to the coefficient of friction and the normal force.

In this case the penny is sitting on the surface and the gravitational force is equal in size to the normal force.  Therefore 

The force of gravity is equal to the mass times the gravitational acceleration.

We can put all this together to a larger equation that says that

Notice that mass falls out of both sides of the equation

We can now rearrange and solve for the coefficient of friction

Now we can plug in our known values

In circular motion, velocity is tangential to the circular path. Since the object is moving counterclockwise, at the top of the circle this tangent line points to the left. It may help to draw a diagram to better visualize this motion.

Velocity is given by distance per unit time.

When moving in a circle, the distance is the circumference, and each rotation takes exactly one period. We can substitute into the velocity formula.

If the children are in a straight line, that means that their periods (how long it takes to make one revolution) will be the same. The only thing that changes is r, the distance from the center. Since radius is in the numerator, we can conclude that increasing the distance from the center will increase the velocity.

Velocity is given by distance per unit time.

When moving in a circle, the distance is the circumference, and each rotation takes exactly one period. We can substitute into the velocity formula.

If the children are in a straight line, that means that their periods (how long it takes to make one revolution) will be the same. The only thing that changes is , the distance from the center. Since radius is in the numerator, we can conclude that increasing the distance from the center will increase the velocity.

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.

Centripetal acceleration is the acceleration towards the center when an object is moving in a circle. Though the speed may be constant, the change in direction results in a non-zero acceleration.

The formula for this is , where  is the perceived tangential velocity and  is the radius of the circle.

Plug in the given values and solve for the acceleration.

Centripetal force is the force that constantly moves the object towards the center; it is what keeps the object moving in a circle rather than flying off tangentially to the circle.

The formula for force is .

To find the centripetal force, we need to find the centripetal acceleration. We do this with the formula , where  is the perceived tangential velocity and  is the radius of the circle.

Plug in the given values and solve for the acceleration.

Plug that into the first equation to solve for the force.

The period, , of an object moving in circular motion is the amount of time it takes for the object to make one complete loop of the circle.

If we start with the linear understanding of velocity,, we can apply the same concept here. Our velocity should be the change in distance over the change in time. In this case, we don't have a definite time, , but we do have a period in terms of one complete loop.

We can set up an equation for the period using the circumference of the circle as our distance: .

Plug in the given values to solve for the period.

Centripetal acceleration is the acceleration towards the center when an object is moving in a circle. Though the speed may be constant, the change in direction results in a non-zero acceleration.

The formula for this is , where  is the perceived tangential velocity and  is the radius of the circle.

Plug in the given values and solve for the acceleration.

Centripetal force is the force that constantly moves the object towards the center; it is what keeps the object moving in a circle rather than flying off tangentially to the circle.

The formula for force is .

To find the centripetal force, we need to find the centripetal acceleration. We do this with the formula , where  is the perceived tangential velocity and  is the radius of the circle.

Plug in the given values and solve for the acceleration.

Plug the acceleration and given mass into the first equation to solve for force.