Question

A common amusement park ride is a Ferris wheel (not drawn to scale). Riders sit in chairs that are on pivots so they remain level as the wheel turns at a constant rate.

A particular Ferris wheel has a radius of 24 meters, and it makes one complete revolution around its axle (at location A) in 20 seconds. In all of the following questions, consider locationA (at the center of the axle) as the location around which we will calculate the angular momentum. At the instant shown in the diagram, a child of mass 34 kg, sitting at location F, is traveling with velocity < -7.5, 0, 0> m/s.

What is the momentum of the child?
=kg·m/s

In the definition  what is the vector ?
=m

What is ?
= m

What is the magnitude of the angular momentum of the child, about location A?
= kg·m²/s

Use the right-hand rule to determine the z-component of the angular momentum of the child, about location A:
= kg·m²/s

You used the right-hand rule to determine the z-component of the angular momentum, but as a check, calculate  in terms of position and momentum:
What is ?
= kg·m²/s

What is ?

= kg·m²/s

What is the z-component of the angular momentum of the child, about location A?
= kg·m²/s

The Ferris wheel keeps turning, and at a later time, the same child is at location E, with coordinates < 16.971, -16.971, 0 > m relative to location A, moving with velocity < -5.303, -5.303, 0 > m/s.

Now what is ?
= kg·m²/s

What is ?
= kg·m²/s

What is the z-component of the angular momentum of the child, about location A?
= kg·m²/s

Answer 1

Solution in the uploaded image