- #1
21joanna12
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Homework Statement
There is a point particle on the edge of a merry-go-round. It has mass 15kg and the merry-go-round has mass 235kg. The initial angular momentum is 2 radians per second. If the point particle moves from the outer edge of the merry-go round to the centre, what is the final angular momentum?
I've tried to do this problem using conservation of angular momentum and conservation of rotational kinetic energy and I get two different answers...
Homework Equations
moment of inertia of particle, Ip = mr2 and of merry-go-round, Im=mr2/2
rotational kinetic energy =Iω2/2
Angular momentum, L=Iω for particle or
The Attempt at a Solution
In both cases, the moment of inertia of the partcle in the centre is zero and therefore its rotational kinetic energy and angular momentum are zero .
First, using conservation of angular momentum,
intial angular momentum of merry go round + of particle = final angular momentum of merry-go-round.
0.5x235xr2x2 + 15xr2x2 = 0.5x235xr2xωfinal
235 + 30 = 0.5x235xωfinal
ωfinal= 2.2553...
Using conservation of rotational kinetic energy,
0.5x15xr2x22 + 0.5x0.5x235xr2x22 = 0.5x0.5x235xωfinal2
Then I get ωfinal= 2.1238...
I have a feeling that the issue may be that the rotational KE of the particle isn't zero even when it is at the centre, although I'm not sure...
Thank you in advance! :)