A merry go round rotates at the rate of 0.20 rev/s with an 80kg man standing at

Question

A merry go round rotates at the rate of 0.20 rev/s with an 80kg man standing at a point 2.0m from the axis of rotation.
(a) What is the new angular speed when the man walks to a point 1.0m from the center? Assume that the merry go round is a solid 25kg cylinder of radius 2.0m.
(b) Calculate the change in kinetic energy due to the man's movement. How do you account for this change in kinetic energy

I had a hard time understanding the explanation in the problem that was already done. I didn't under stand where the 130kg came from

Explanation / Answer

this is a conservation of angular momentum question!

the moment of inertia of a solid cylinder is:
I = mr2/2

the moment of inertia of a point particle (we'll assume the man isa point particle) is:
I = mr2

initially, the moment of inertia of the system is:
I0 = Icylinder +Iman
=mcrc2/2 +mmanrman2
= 25kg * (2.0m)2 / 2 +80kg * (2.0m)2
= 370kgm2

the final moment of inertia is:
If =mcrc2/2 +mmanrman2
= 25kg * (2.0m)2 / 2 + 75kg *(1m)2
= 125 kgm2

a)
first convert 0.20rev/s to rad/s because that is what you want your answer in:
0.20rev/s * 2rad/rev = 0.4 rad/s

now equate the initial and final angular momenta:
L0 = Lf
I00 =Iff
f =I0 0/If = 370kgm2* (0.4)rad/s / 125kgm2
= 3.718 rad/s

b)
the change in kinetic energy is the difference between the initial and final rotational kinetic energies:
E =0.5I2

E = Ef - E0
= 0.5 *125 kgm2 * (3.718 rad/s)2 - 0.5 *370kgm2 * (0.4rad/s)2
= 571.83 J

c)
The moment arm of the man about the axis of rotation decreases.
this can't be true because E > 0
since E varies as r2,then if r decreases, then E must also decrease
we found the opposite to be thecase
Work is done by themerry-go-round on the man as he moves towards the center.
not true because the merry-go-round didn't do anything
Wind resistance varies as the square of the speed.
I think this one is obviously not true...

the answer is :
Work is done by the man on the system as he moves towards the center

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