Question

A torque of magnitude 1000 nm acting on body produces an angular acceleration of 2 rad/s2. Calculate the moment of inertia of the body.

Answer 1

Answer:

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Answer 2

Answer:

The body has a moment of inertia of 500 kg-m².

Explanation:

• The force that makes an object rotate about its axis is called torque.
• It's a vector quantity unit Newton-meter as its S.I unit.
• The direction of the force applied on the axis decides the direction of the torque vector.
• The time rate of change of angular velocity is said to be angular acceleration.
• It is usually denoted by ∝ and expressed as radians per second.
• The expression of angular acceleration is :

                                                 ∝ =Δω/Δt

where,         Δω = change in angular velocity

                   Δt = change in time

• The rotational inertia of the body is said to be the moment of inertia.
• It is expressed by kg-m² and in terms of torque the moment of inertia is written as;

                      Moment of inertia (I) = Torque (ζ)/Acceleration(a)

                                ∴      $I=\frac{1000}{2}$

                                           =500 kg-m²

Therefore the body has a 500 kg-m² moment of inertia in the given conditions.