Question

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·m^{2} 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·m^{2} 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?

Answer #1

Given: First Disk, Rotational inertia I_{1} = 3.88
kgm^{2}

Angular velocity (_{1})
= 176 rev./min

Second Disk, Rotational Inertia I_{2} = 7.15 kg
m^{2}

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

I_{1}_{1}
+ I_{2}_{2}
= (I_{1}+I_{2})
_{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 .

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