Question

Which of the following represents the torque? (symbols have usual meanings) Orxp O FX da Both (2) and (3)​

Answer 1

Answer:

option 2

Explanation:

r vector x F vector

Answer 2

Torque is the measure of the force which is needed to rotate an object about its axis. It is formulated by the cross product of distance vector and Force vector or as the differentiated product of Angular Momentum with respect to time.

• Torque (τ) is the cross product of the perpendicular distance between the point of contact and the point at which force is applied and the magnitude of force applied. Hence,

                                    τ = r × F              (1)

• Angular Momentum (L) is is the rotational analogue of linear momentum. It is calculated by the cross product of distance between point of contact and application of force and linear momentum.

                       L = r × p = mvr                 ( mass × velocity × distance)

• Torque can also be calculated by differentiating L by time.

                     $\frac{dL}{dt}$ = $\frac{d(mvr)}{dt}$

                ⇒ $\frac{dL}{dt}$ = mr × $\frac{dv}{dt}$                    (mass and distance are constants)

               ⇒ $\frac{dL}{dt}$ =   mr × a = r × F         (acceleration = $\frac{dv}{dt}$ and F = ma)

               ∴ $\frac{dL}{dt}$ = τ

Hence, only option (2) r x F is correct.