1. Calculate the moment of inertia of this disk for rotations about its axle, in
ID: 2181255 • Letter: 1
Question
1. Calculate the moment of inertia of this disk for rotations about its axle, in kg m2.
2. Another disk has the same shape and size as the one in the previous question, but is made instead of brass. The density of brass is 8.70 g/cm3. What is the ratio between the two moments of inertia, Ibrass : Ialuminum?
3. Now imagine that the brass disk is placed horizontally and that it is set to rotate without friction about its (vertical) axle with angular speed w0. Then, the aluminum disk is dropped on top of the rotating brass disk, and due to the friction between both, after a very short time they are both rotating together with angular speed wf. You can solve this question using conservation of angular momentum. Why is that?
a. Because the force between the wheel and the disk is zero.
b. Because the weight of the disk is negligible.
c. Because the friction force by the wheel on the disk is negligible.
d. Because the net external torque on the wheel + disk system is negligible.
e. Because the torque by the wheel on the disk is negligible.
f. Because the torque by the weight of the disk is zero.
4. What is the ratio between the final and initial angular speeds, wf :w0?
Explanation / Answer
moment of inertia for a solid disk = 0.5mr^2, so ratio of inertia of 2 disks = m1/m2(since r1 = r2). as mass = volume x density, and volume of both disks is same, m1/m2 = d1/d2., so Inertia of disk 1/ Inertia of disk 2 = density of aluminium /density of brass. use density of aluminium to calculate this. _________________________________________________________________________ we can use conservation of angular momentum because there is no external torque. _________________________________________________________________________ Inertia of disk 1 x w0 = (Inertia of disk 1 + Inertia of disk 2) x wf, so m1r^2 w0 = r^2(m1 + m2)wf, so w0/wf = (m1 + m2)/m1
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