Question
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?
B. calculate the change in kinetic energy due to man moving
C. how do you account for this change in kinetic energy?
Answers
drwls
We will gladly critique your work
Rachel
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 :)