Rotational Motion Part 1

When two small spheres of mass m are attached gently, the external torque, about the axis of rotation, is zero.
So, ‌

d → L

dt

=z=0

→

L

= conserved
So the angular momentum about the axis of rotation is conserved.
∴I1ω1=I2ω2
⇒ω2=‌

I1

I2

ω1
Here Moment of inertia of Disc I1=‌

1

2

MR2 and
After adding two sphere Moment of Inertia of disc and two sphere,
I2=‌

1

2

MR2+2(‌

1

2

mR2+‌

1

2

mR2)
∴ω2=‌

‌ 1 2 MR2

1 2 MR+2mR2

×ω1=‌

M

M+4m

ω1