A disc with moment of inertia 1.5 kg m2 is rotating with an angular speed of 800 rev/min on a shaft. A second disc, initially at rest and with moment of inertia 5.0 kg m2,is suddenly clamped together to the same shaft. (a) Determine magnitude of angular momentum of the first disc.
(b) Determine the common angular speed of the combination of the two discs.

Explanation:

Angular momentum p = Iw

I is the moment of inertia

w is the angular velocity

a) Angular momentum of the first disc

p1 = I1w1

Given

I1 = 1.5kg/m²

w1 = 800rev/min

Convert to rad/s

1 rev = 6.283rad

1 min = 60secs

800rev/min = 800(6.283)/60

= 83.77rad/s

p1 = 1.5×83.77

p1 = 125.66kgrad/s

Hence the magnitude of angular momentum of the first disc is 125.66kgrad/s

b) according to law of conservation of momentum

I1w1+I2w2 = (I1+I2)w

w is the common angular speed

Given

11w1 = 125.66

w2 = 0rad/s

I1 = 1.5kgm²

I2 = 5kgm²

Substitute

125.66+0 = (1.5+5)w

125.66 = 6.6w

w = 125.66/6.5

w = 19.33rad/s

Since 1rad/s = 9.549tev/min

19.33rad/s = 184.6rev/min

Hence the common angular speed of the combination of the two discs is 184.6rev/min

no. dot product   =0 when vecs at right angles