A 33kg child named Lindsey runs as fast as she can and jumps onto the outer edge of a merry-go-round. The merry-go-round is initially at rest and has a mass of 78kg and a radius of 2.20m. Lindsey's linear velocity was 9 m/s at the moment she jumped onto the merry-go-round.

Question

What is the initial angular momentum?

I am using the formula 1/2 mr^2 * w(initial).

Whatever I do is wrong, and I'm not sure if it is because I have the wrong formula or because I am not converting units properly..

Answer 1

Circumference = pi*2r = 3.14 * 4.4 = 13.8 m.

Va = 9m/s * 6.28rad/13.8m = 4.1 rad/s. = Angular velocity.

Answer 2

Momentum = M*Va = 33 * 4.1 = 135.2.

Answer 3

You have the wrong formula. The equation you're using for angular momentum calculates the moment of inertia for the merry-go-round (disk), not Lindsey. As the question states, "Hint: Although she started with linear velocity, consider the moment JUST BEFORE she landed on the merry-go-round." Therefore, we need to use an equation that calculates the moment of inertia for Lindsey. This would be: L= m(r^2)w. Since w=v/r, the final equation can be simplified to: L=mrv.