the dimensions of torque are the same as those of energy. Why it would nevertheless be inappropriate to measure torque in joules.
Energy is force x distance, where distance is the distance in the direction of force. Torque is force x distance perpenduclar to force.
Joules is a measure of energy. Torque is rotational force, not energy.
To understand why it is inappropriate to measure torque in joules, we need to consider the definitions and dimensions of torque and energy.
Torque is defined as the rotational force applied to an object, resulting in a rotational motion. It is a vector quantity that involves both the force applied and the distance from the axis of rotation. The formula for torque is given as torque = force x distance (perpendicular to the force). The SI unit for torque is the newton-meter (N∙m).
Energy, on the other hand, is the capacity of a system to do work. It is a scalar quantity that represents the ability to cause change or produce an effect. The formula for energy is given as energy = force x distance (in the direction of the force). The SI unit for energy is the joule (J).
Although both torque and energy have the same dimensions (force x distance), they have different physical meanings and applications. Torque is specifically related to rotational motion, while energy is a more general concept that can be associated with various types of work or motion.
It would be inappropriate to measure torque in joules because torque and energy are distinct concepts with different physical interpretations. Using joules as the unit for torque could lead to confusion and misinterpretation of the actual rotational force being applied. Therefore, torque is measured in newton-meters to accurately represent its rotational nature and distinguish it from energy.