Class 11 Physics Rotational Motion Torque & Angular Momentum

Torque & Angular Momentum

  • The rotational analogue of force is moment of force (Torque).
  • If a force acts on a single particle at a point P whose position with respect to the origin O is given by the position vector r the moment of the force acting on the particle with respect to the origin O is defined as the vector product t = r × F =  rF sinΘ

  • Torque is vector quantity.
  • The moment of a force vanishes if either
  • The magnitude of the force is zero, or
  • The line of action of the force (r sinΘ) passes through the axis.

Example: Determine the torque on a bolt, if you are pulling with a force F directed perpendicular to a wrench of length l cm?

Solution:  t = r x F = rF sinΘ

In this case Θ=90o

 

 

  • The quantity angular momentum is the rotational analogue of linear momentum.
  • It could also be referred to as moment of (linear) momentum.
  • l = r × p
  • Rotational analogue of Newton’s second law for the translational motion of a single particle:  dl/st = τ

Torque and angular momentum of system of particles:

  • The total angular momentum of a system of particles about a given point is addition of the angular momenta of individual particles added vectorially.

           

  • Similarly for total torque on a system of particles is addition of the torque on an individual particle added vectorially.
  • The torque resulting from internal forces is zero , due to
  • Newton’s third law i.e. these forces are equal and opposite.
  • These forces act on the line joining any two particles 
  • The time rate of the total angular momentum of a system of particles about a point is equal to the sum of the external torques acting on the system taken about the same point.  

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