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.