The moment of inertia of a body is 100 kg-m². If 50 N-m torque is applied on this body, then find the angular acceleration produced in the body.

CONCEPT:

Torque:

• Torque is a physical quantity that can cause an object to rotate about an axis.
• Force is what causes an object to accelerate in linear kinematics. Similarly, torque is what causes an angular acceleration. Hence, torque can be defined as the rotational equivalent of linear force.
  • Torque is a vector quantity.
  • Its SI unit is N-m.
• If F force is acting at a distance r from the axis of rotation at an angle θ as shown in the figure, then the torque is given as,

​⇒ τ = F.r.sinθ

• If I and α are the moment of inertia and the angular acceleration respectively, then torque acting on the body is given as,

⇒ τ = Iα

CALCULATION:

Given I = 100 kg-m2, and τ = 50 N-m

• If I and α are the moment of inertia and the angular acceleration respectively, then torque acting on the body is given as,

​⇒ τ = Iα     -----(1)

By equation 1 the angular acceleration produced in the body is given as,

⇒ α = 0.5 rad/sec²

• Hence, option 2 is correct.