Rotational Motion Part 1

The moment of inertia of the rod about O is ‌

1

2

mℓ2. The maximum angular speed of the rod is when the rod is instantaneously vertical. The energy of the rod in this conditions is ‌

1

2

Iω2 where I is the moment of inertia of the rod about O. when the rod is in its extreme portion, its angular velocity is zero momentarily. In this case, the center of mass is raised through h, so the increase in potential energy is mgh. This is equal to kinetic energy ‌

1

2

Iω2.
∴mgh=‌

1

2

Iω2=‌

1

2

(‌

1

3

ml2)ω2
⇒h=‌

ℓ2ω2

6g