Question

# Two disks are mounted (like a merry-go-round) on low-friction bearings on the same axle and can...

Two disks are mounted (like a merry-go-round) on low-friction bearings on the same axle and can be brought together so that they couple and rotate as one unit. The first disk, with rotational inertia 3.88 kg·m2 about its central axis, is set spinning counterclockwise (which may be taken as the positive direction) at 176 rev/min. The second disk, with rotational inertia 7.15 kg·m2 about its central axis, is set spinning counterclockwise at 823 rev/min. They then couple together. (a) What is their angular speed after coupling? If instead the second disk is set spinning clockwise at 823 rev/min, what are their (b) angular velocity (using the correct sign for direction) and (c) direction of rotation after they couple together?

Given: First Disk, Rotational inertia I1 = 3.88 kgm2

Angular velocity (1) = 176 rev./min

Second Disk, Rotational Inertia I2 = 7.15 kg m2

Angular velocity (2) = 823 rev/min

We will use conservation of angular momentum for this problem. So, change in angular momentum will be zero.

a)

Angular momentum of first disk + Angular momentum of second disk = Angular momentum of combined disks

I11 + I22 = (I1+I2) f

(3.88×176 ) + (7.15×823) = ( 3.88+7.15)×f

f = 595.406 rev/min.

b) as we assume counter clockwise to be positive. So here , in this case second disk is rotating in negative direction .

2 = - 823 rev/min.

So , (3.88×176)-(7.15×823) = (3.88+7.15) f

f = - 471.58 rev/min.

c) hence direction of rotation after they coupled is clockwise .