Final answer:
Torque about the origin is calculated as the cross product of the position vector and the force vector, representing how a force causes rotation about an axis, in this case, the origin. Torque is related to angular momentum as it is the time derivative of angular momentum.
Step-by-step explanation:
Understanding Torque About the Origin
When discussing the torque about the origin, we are referring to the rotational counterpart to force. It measures how effectively a force can cause an object to rotate about an axis, in this case, the origin. Torque (τ) is calculated by taking the cross product of the position vector (ρ) and the force vector (F), which gives τ = ρ x F. This involves both the magnitude of the force, the distance of the applied force from the origin (lever arm), and the angle between the force and the lever arm.
For example, if the force (5.0â - 2.0ç + 1.0Ç) N is applied at the point whose position vector is Ρ = (−2.0â + 4.0ç) m, we would calculate the torque on the particle by finding the cross product of these two vectors.
The general relationship between torque and angular momentum (L) is that torque is the time derivative of angular momentum: τ = dL/dt