- #1
robert6774
- 5
- 0
Four children stand at the edge of a circular horizontal platform that is free to rotate about a vertical axis. Each child has a mass of 35 kg and they are at positions that are a quarter-circle from each other. The platform has a moment of inertia equal to 500 kg*m^2 and a radius of 2.0 m. The system is initially rotating at 6.0 rev/min. The children walk towards the center of the platform until they are 0.50 m from the center.
m= 35 kg
I= 500 kg*m^2
r1= 2.0 m
w(initial)= 6.0 rev/min or 0.628 rad/s (correct me if I'm wrong)
r2= 0.50 m
(a) What is the rotational speed of the platform when the children are at the 0.50 m positions?
(b) What is the change in kinetic energy of the system?
Here are a few equations I might need to use:
w= d(theta)/dt
a= dw/dt
w= w(initial)+at
(theta)= w(initial)t + 1/2at^2
2a(theta)= w^2 - w(initial)^2
s=r(theta)
a= w^2r
K= 1/2 Iw^2
I don't think I should bring time as a variable into the picture because it would make it more things more complicated. I don't really know where to start. The only thing I've really done so far is write down the givens and draw a diagram. Thats a lot of equations but I know I don't need them all.
I tried using a= w^2r but I ended up with weird units. Maybe I don't understand the equation. So it would be (6.0)^2(2.0)= 72 rev/min*m. What?
The thing is I feel as though I'm missing one too many variables. When I try to utilize an equation, I can't solve it. For example, when I try to use w= w(initial)+at I'm missing both the acceleration and the time. When using 2a(theta)= w^2 - w(initial)^2 I'm missing teh acceleration and theta.
Because my only lead with a= w^2 isn't working, I'm stuck.
Any help and guidance would be very much appreciated, thank you.
m= 35 kg
I= 500 kg*m^2
r1= 2.0 m
w(initial)= 6.0 rev/min or 0.628 rad/s (correct me if I'm wrong)
r2= 0.50 m
(a) What is the rotational speed of the platform when the children are at the 0.50 m positions?
(b) What is the change in kinetic energy of the system?
Here are a few equations I might need to use:
w= d(theta)/dt
a= dw/dt
w= w(initial)+at
(theta)= w(initial)t + 1/2at^2
2a(theta)= w^2 - w(initial)^2
s=r(theta)
a= w^2r
K= 1/2 Iw^2
I don't think I should bring time as a variable into the picture because it would make it more things more complicated. I don't really know where to start. The only thing I've really done so far is write down the givens and draw a diagram. Thats a lot of equations but I know I don't need them all.
I tried using a= w^2r but I ended up with weird units. Maybe I don't understand the equation. So it would be (6.0)^2(2.0)= 72 rev/min*m. What?
The thing is I feel as though I'm missing one too many variables. When I try to utilize an equation, I can't solve it. For example, when I try to use w= w(initial)+at I'm missing both the acceleration and the time. When using 2a(theta)= w^2 - w(initial)^2 I'm missing teh acceleration and theta.
Because my only lead with a= w^2 isn't working, I'm stuck.
Any help and guidance would be very much appreciated, thank you.