Torque can be defined as the rate of change of angular momentum, analogous to force. The net external torque on any system is always equal to the total torque on the system; in other words, the sum of all internal torques of any system is always 0 (this is the rotational analogue of Newton’s Third Law).

Torque is the rotational equivalence of linear force. Speed measures the distance covered in unit time. The relation between torque and speed are inversely proportional to each other. The torque of a rotating object can be mathematically written as the ratio of power and angular velocity.

A torque is a force applied to a point on an object about the axis of rotation. The size of a torque depends on (1) the size of the force applied and (2) its perpendicular distance from the axis of rotation (which depends both on the direction of the force plus its physical distance from the axis of rotation).

The SI unit for torque is Newton- meter as we know that the unit of force is newton which is equal to Force=mass×acceleration. The SI unit of mass is Kilogram and acceleration is meter/sec2. Hence the dimensional formula of torque is ML2T−2.

A force involves the product of mass and acceleration. Mass is a base quantity having a dimension of M. Putting all these together, we have the dimension for both dot product (work) and cross product (torque) to be ML²T⁻². Yes, they have the same dimensions in this sense.

The dimensional formula associated with energy is [ML2T-2] and the dimensional formula for frequency is [T-1]. So the dimensional formula for Planck’s constant is [ML2T-1]. So the dimensional formula for angular momentum is [ML2T-1].

Thus the Earth moves through angle 2/pi radians in 365 days. Angular frequency is a scalar quantity, it means it is just a magnitude….Angular Frequency Formula.

Relative density, refractive index and Poisson ratio all the three are ratios, therefore they are dimensionless constants.

Gravitational constant. Hint: The physical quantities which have dimensions and have a fixed value are called dimensional constant.

Strain is a dimensionless quantity. Strain is defined as extension per unit length. Strain has no units because it is a ratio of lengths.

But the ratio of the internal to the viscous forces is dimensionless, so it must depend on some combination of the viscosity, speed V and linear size l that is dimensionless. It is easy to see that VIV – or any power of it, positive, negative, zero, integral, nonintegral – is dimensionless.

A dimensionless variable is a unitless value produced by multiplying and dividing combinations of physical variables, parameters, and constants. As strain is ratio of change in variable divided by same variable, it’s also a dimensionless quantity.

Dimensionless variables can reduce these figures drastically. A dimensionless variable (DV) is a unitless value produced by (maybe repeatedly) multiplying and dividing combinations of physical variables, parameters, and constants.