The dimension of angular impulse is

The correct answer is [ML²T^-1].

Key Points

• Angular impulse is defined as the product of torque and the time duration over which it acts.
• The formula for angular impulse is: Angular Impulse = Torque × Time.
• The dimensional formula for torque is [ML²T^-2], and time has a dimension of [T].
• Multiplying the dimensions of torque and time gives: [ML²T^-1].
• Hence, the dimension of angular impulse is [ML²T^-1], which matches Option 3 in the given question.

Additional Information

• Torque:
  • Torque is the rotational equivalent of force, causing an object to rotate around an axis.
  • Its formula is Torque = Force × Perpendicular Distance.
  • The dimensional formula of torque is [ML²T^-2].
• Angular Momentum:
  • Angular momentum is the rotational analog of linear momentum.
  • It is given by Angular Momentum = Moment of Inertia × Angular Velocity.
  • The dimensional formula of angular momentum is also [ML²T^-1].
• Impulse:
  • Impulse is the product of force and the time duration it acts over.
  • The dimensional formula for impulse is [MLT^-1].
  • Angular impulse is the rotational analog of linear impulse.
• Conservation of Angular Momentum:
  • Angular momentum of a system remains constant if no external torque acts on it.
  • This principle is crucial in understanding the dynamics of rotating systems like planets, satellites, and spinning objects.