A merry-go-round with r = 4m and a perfect frictionless bearing is pushed with a force of 24 N by a young girl. She pushes with a constant force that is oriented tangentially to the edge of the merry-go-round. After she pushes the merry-go-round through 14 full rotations (at which point she lets go) it is spinning with an angular speed of 3 rad/s.
a. What is the moment of inertia of the merry-go-round?
b. After the girl lets go, a 20 kg boy jumps onto the merry-go-round and sticks halfway between the center of the edge. How fast are the merry-go-round and the boy spinning after he lands?
Physics - Damon, Monday, April 23, 2012 at 8:26pm
ah, it turns out I took this course in 1955 and have had lots of practice since. I do not need to do your homework. However you do. Try the problems then comeback to us with specific things you are stuck on.
The first part is moment or torque = moment of inertia * angular acceleration, alpha
with constant alpha:
omega = omega initial + alpha * t
angle = initial angle + omega initial*t + (1/2) alpha * t^2
The second part is conservation of angular momentum with the moment of inertia increased by the mass of the boy times the square of distance from center.
Physics - Damon, Monday, April 23, 2012 at 8:30pm
By the way to find the time it is easy to use the average velocity (3/2 = 1.5 radians/sec) for 14 *2 pi radians