Question

What is the difference between ‘torque’ and ‘work’?

Answer 1

Hint : Torque is the rotational equivalent of linear force which causes an angular acceleration and angular acceleration is the rate of change of the angular velocity with respect to the time. Work can be defined as the product of force and distance travelled. Here we are going to understand the difference between both the terms thoroughly.

Complete Step By Step Answer:
Torque – Torque is the vector quantity. It is the rotational force which causes an object to rotate about an axis.
$\overrightarrow \tau = \overrightarrow r \times \overrightarrow F$
Where, “r” is measured in meters and “F” is measured in Newton
Dimensions of torque $\left[ \tau \right] = \left[ r \right] \times \left[ F \right]$
Dimensions of torque $\left[ \tau \right] = \left[ {{L^1}} \right] \times \left[ {{M^1}{L^1}{T^{ - 2}}} \right]$ (When base are same, powers are added)
Dimensions of torque $\left[ \tau \right] = \left[ {{M^1}{L^2}{T^{ - 2}}} \right]$...... $(1)$
Torque is expressed as the angular motion.
Work – Work is the scalar quantity. Work is said to be done when the object moves the certain distance when the force is applied.
$W = F \times d$
Force is measured in Newton or kilogram into metre per second square and the displacement is measured in metre.
Dimensions of Work $\left[ W \right] = \left[ F \right] \times \left[ d \right]$
Dimensions of Work $\left[ W \right] = \left[ {{M^1}{L^1}{T^{ - 2}}} \right] \times \left[ {{L^1}} \right]$
Dimensions of torque $\left[ W \right] = \left[ {{M^1}{L^2}{T^{ - 2}}} \right]$ ........... $(2)$
Work is expressed as linear motion.

Note :
Torque is always required to create an angular acceleration of any object. Torque can also be referred to as the moment or moment of force or the rotational force or the turning effect. In case of the constant rotational inertia of the object, the angular acceleration is directly proportional to the torque. Both the terms torque and the work have the same dimensional quantity and expressed as the unit as Newton into metre, but only work can be expressed as its SI unit as the Joules.