For the following 5 problems use 6. Two disks are mounted on low-friction bearin

Question

For the following 5 problems use 6. Two disks are mounted on low-friction bearings on the same axle and can be brought together so that they couple and rotate as one unit. a. The first disk, with rotational inertia 3.3.kg m^2 about its central axis, is set spinning at 450 rev/min. The second disk, with rotational inertia 6.6 kg m^2 about its central axis is set spinning at 900 rev/min in the same direction as the first. They couple together. What is their angular speed after coupling? b. If instead the second disk is set spinning at 900 rev/min in the direction opposite the first disk's rotation, what is the angular speed after coupling?

Explanation / Answer

a)

I1 = 3.3 Kg.m^2

I2 = 6.6 Kg.m^2

w1 = 450 rpm

w2 = 900 rpm

Here , we will use the conservation of angular momentum ,

Let the final angular velocity be w

I1*w1 + I2*w2 = (I1+I2)*w

w*(3.3 + 6.6) = 3.3 *450 + 6.6*900

w = 750 rpm

the final angular speed is 750 rev/min

B)

Now ,

For oposite direction ,

I1 = 3.3 Kg.m^2

I2 = 6.6 Kg.m^2

w1 = -450 rpm

w2 = 900 rpm

Here , we will use the conservation of angular momentum ,

Let the final angular velocity be w

I1*w1 + I2*w2 = (I1+I2)*w

w*(3.3 + 6.6) = -3.3 *450 + 6.6*900

w = 450 rpm

the final angular speed is 450 rev/min in the direction of second disk

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---