The resulting angular speed = 0.6 rad / s.
<u>Explanation:</u>
Here there is no external torque acting on the system thus we can apply the law of conservation of angular momentum
Angular momentum of the man = Iω
Where I = Inertia of the man about the axis of rotation
or I = M r 2
I = 50 * 1.25*1.25 = 78.125
w = Angular velocity of the man, that can be calculated as follows
Tangential velocity of man = v = 2m/s
So time taken to describe this circle is t = (2*pi* r) / v
Now angle described in 1 revolution θ = 2*pi radians
This angle is subtended in time t = (2*pi* r) / v
Thus angular speed = w = θ/t = 2*pi* ( v/ 2π r) = v/r = 2.70 / 1.25 = 2.16 rad/s
So angular momentum of man = Iw = 78.125 * 2.16 = 168.75.
To conserve the angular momentum before and after,
Angular momentum of disk = angular momentum of the man
i.e. Iw of disk = 168.75
disk of I = (disk of M*R^2) / 2
= (1.00 * 102 * 2.30 * 2.30) / 2
= 269.79
Thus 269.79 of disk of w = 168.75
Resulting angular speed of disk = 168.75 / 269.79 = 0.6 ras / s
