A merry-go-round rotates at the rate of.2rev/s with an 80kg man standing at a point 2m from the axis ofrotation. (A)What is the new angular speed when the man walksto a point 1m from the center? Assume that the merry-go-round is a solid 25kg cylinder of radius of 2m.
B. calculate the change in kinetic energy due to man moving
C. how do you account for this change in kinetic energy?
2 answers
We will gladly critique your work
angular momentum (L) = Inertia (I) * angular velocity (w)
Using conservation of angular momentum (L):
Inertia initial total (Ii) * angular velocity initial (wi) = Inertia final total (If) * angular velocity final (wf)
Inertia of disks (such as the merry-go-round) = .5 * mass (m) * radius squared (r)
Inertia of a point-mass (such as the person) = m * r^2
with this you should get the following:
Li=Lf
Ii*wi=lf*wf
(I + Ii)*wi=(I + If)*wf
(.5MR^2 + mri^2)wi=(.5MR^2 + mrf^2)wf
where
M=mass of the merry-go-round
R=radius of the merry-go-round
m=mass of the person
ri=initial radius of the person
re-arrange and solve for wf for part a
*********************************************
change in KE(rotational) is KEf-KEi
KE(rot) = .5*I*w^2
you should get a positive change. This makes sense because if you think of radius between the person and the pivot-point as the distance associated with Potential Energy, as the distance decreases, the speed along with Kinetic energy should increase due to conservation of energy.
PEi + KE(rot)i = PEf + KE(rot)f
big + small = small + big
change in KE = big - small = positive change
I hope that makes sense :)
Using conservation of angular momentum (L):
Inertia initial total (Ii) * angular velocity initial (wi) = Inertia final total (If) * angular velocity final (wf)
Inertia of disks (such as the merry-go-round) = .5 * mass (m) * radius squared (r)
Inertia of a point-mass (such as the person) = m * r^2
with this you should get the following:
Li=Lf
Ii*wi=lf*wf
(I + Ii)*wi=(I + If)*wf
(.5MR^2 + mri^2)wi=(.5MR^2 + mrf^2)wf
where
M=mass of the merry-go-round
R=radius of the merry-go-round
m=mass of the person
ri=initial radius of the person
re-arrange and solve for wf for part a
*********************************************
change in KE(rotational) is KEf-KEi
KE(rot) = .5*I*w^2
you should get a positive change. This makes sense because if you think of radius between the person and the pivot-point as the distance associated with Potential Energy, as the distance decreases, the speed along with Kinetic energy should increase due to conservation of energy.
PEi + KE(rot)i = PEf + KE(rot)f
big + small = small + big
change in KE = big - small = positive change
I hope that makes sense :)
0 answers