Question

While riding the merry-go-round at the playground, Monique, who has a mass of 45 kg, is traveling at a speed of 90 m/s, Her angular momenturn is 810 kg m%ls. How far is she sitting from the center of the merry go round?

Answer 1

To find the distance that Monique is sitting from the center of the merry-go-round, we can use the formula for angular momentum. First, we calculate Monique's angular velocity using the given angular momentum and moment of inertia. Then, we use the angular velocity to find the linear velocity, which can be used to calculate the distance from the center.

Step-by-step explanation:

To calculate the distance Monique is sitting from the center of the merry-go-round, we can use the formula for angular momentum.

Angular momentum is given by the equation L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

We are given Monique's mass and angular momentum, so we can find her angular velocity using the equation ω = L / I. Once we have the angular velocity, we can use it to find the distance from the center of the merry-go-round using the formula v = ωr, where v is the linear velocity and r is the radius.

Plugging in the values, we get ω = 810 kg m^2/s / (45 kg * m^2) = 18 rad/s. Then, using the equation v = ωr, we can find the distance: v = 18 rad/s * 1.8 m = 32.4 m.