Question

A roundabout is a type of playground equipment involving a large flat metal

disk that is able to spin about its center axis. A roundabout of mass 120kg has

a radius of 1.0m is initially at rest. A child of mass 43kg is running toward the

edge of the roundabout (meaning, running on a path tangent to the edge) at

2.7 m/s and jumps on. Once she jumps on the roundabout, they move together

as a single object. Assume the roundabout is a uniform disk.

1. What is the magnitude of her angular momentum (with respect to the

center of the roundabout) just before she jumps?

2. What is the angular speed of the roundabout after the jump?

3. Does the overall kinetic energy of the system increase, decrease, or remain

constant? If you say it changed, explain what caused a change in energy

Answer 1

let
M = 120 kg
R = 1.0 m
m = 43 kg
v = 2.7 m/s

1) her angular momentum = m*v*R

= 43*2.7*1

= 116.1 kg.m^2/s <<<<<<<<<<-----------------Answer

2) let w is the angular speed of roundabout after the jump.

apply conservation of angular momentum

Lf = Li

I*w = m*v*R

(0.5*M*R^2 + m*R^2)*w = m*v*R

w = m*v*R/(0.5*M*R^2 + m*R^2)

= 43*2.7*1/(0.5*120*1^2 + 43*1^2)

= 1.13 rad/s <<<<<<<<<<-----------------Answer

3) decreases.

KEi = (1/2)*m*v^2

= (1/2)*43*2.7^2

= 157 J

KEf = (1/2)*I*w^2

= (1/2)*(0.5*M*R^2 + m*R^2)*w^2

= (1/2)*(0.5*120*1^2 + 43*1^2)*1.13^2

= 66 J

clearly KEf < KEi
the loss of kinetic energy is converted as thermal energy.