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. .