Question

Q. what is a relation between torque and moment of inertia⁉️​​

Answer 1

Answer: Torque: Torque is the twisting force that tends to cause rotation

Moment of Inertia:a quantity expressing a body's tendency to resist angular acceleration, which is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation.

Relationship between Torque and Moment of Inertia

For simple understanding, we can imagine it as Newton’s Second Law for rotation. Where, torque is the force equivalent, a moment of inertia is mass equivalent and angular acceleration is linear acceleration equivalent. The rotational motion does obey Newton’s First law of motion.

Consider an object under rotatory motion with mass m, moving along an arc of a circle with radius r. From Newton’s Second Law of motion we know that,

F= ma

⇒a=Fm ———(1)

Substitute linear acceleration a with angular acceleration. That is-

We know that, Acceleration a=ddt(dsdt)

For rotatory motion s = rd??. Thus, Substituting we get-

=ddt(rdθdt) =rddt(dθdt)

Thus, a=rα is the angular acceleration ———-(2)

Simarelly replace force F by Torque ?? we get-

τ=Fr ⇒F=τr ——–(3)

Substituting equation (2) and (3) in (1) we get-

(1)⇒rα=(τr)m ⇒rα=τrm ⇒τ=mr2α

We know that moment of inertia I=mr2

Thus, substituting it in the above equation we get-

⇒τ=Iα

Explanation: