Answer:
A) ω = 13.38 rev/s
B) ω = 9.167 rev/s
C) In clockwise direction
Explanation:
We are given;
Rotational Inertia of first disk; I_1 = 3.76 kg·m²
Angular velocity of first disk; ω_1 = 436 rev/min = 7.267 rev/s
Rotational Inertia of second disk; I_2 = 9.2 kg·m²
Angular velocity of second disk; ω_2 = 953 rev/min = 15.883 rev/s
Total rotational inertia is;
I_total = I_1 + I_2
I_total = 3.76 + 9.2 = 12.96 kg·m²
Now; total angular momentum will be;
L_total = L_1 + L_2
Where L_1 is angular momentum of first disk and L_2 is angular momentum of second disk.
Thus;
I_total•ω = I_1•ω_1 + I_2•ω_2
Plugging relevant values in, we can find their angular speed after coupling which is ω.
Thus;
12.96ω = (3.76 x 7.267) + (9.2 x 15.883)
12.96ω = 173.44752
ω = 173.44752/12.96
ω = 13.38 rev/s
B) since second disk is now spinning clockwise, thus;
I_total•ω = I_1•ω_1 - I_2•ω_2
12.96ω = (3.76 x 7.267) - (9.2 x 15.883)
12.96ω = -118.8
ω = -118.8/12.96
ω = -9.167 rev/s
The negative sign tells us that it is clockwise.
So we would say ω = 9.167 rev/s in clockwise direction
