Question

The moment of inertia of a body about a given axis is 1.2 kgm². Initially, the body is at rest. In order to produce a rotating kinetic energy of 1500 joules, an angular acceleration of 25 rad/s² must be applied about that axis for a duration of:

1. 4 sec
2. 2 sec
3. 8 sec
4. 10 sec

Answer 1

Correct Answer - Option 2 : 2 sec

CONCEPT:

• Moment of Inertia: The moment of inertia plays the same role in rotational motion as mass plays in linear motion. It is the property of a body due to which it opposes any change in its state of rest or of uniform rotation.

  • And the moment of inertia of a particle is given as,

 \(I = m{R^2}\)

• Rotational energy or angular kinetic energy: The kinetic energy in a body due to the rotation of it.

Mathematically expressed by:​

K.E = 1/2 (I × ω2) 

where E is the rotational energy, I is the moment of Inertia and ω is angular velocity.

EXPLANATION:

Given that, I = 1.2 kgm², KE = 1500 joules, ω_o = initial angular velocity = 0

So,​

K.E = 1/2 (I × ω2) 

1500 = 1.2 × ω ²/ 2

ω = 50 rad/sec

Relation between initial and final angular velocity is,

ω = ω_o + αt....(ω_o is initial angular velocity and α = angular acceleratio)

Putting all the values in equation

50 = 0 + 25 × t

t = 50/25 = 2 sec

The correct option is 2 sec.