Write down the formula for work done in rotatory motion.

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Accepted Answer

>

> [!TLDR]
> Work in rotational motion is the rotational analogue of linear work: W = τθ.
>
> **Derivation sketch.** In linear motion, work $dW = F\,dx$. In rotational motion, the analogous relation replaces force with torque $	au$ and linear displacement with angular displacement $d	heta$:
> $$dW = 	au\,d	heta$$
> For a constant torque, integrating from angular position 0 to $	heta$:
> $$W = 	au	heta$$
> …

Linear Quantity	Rotational Analogue
Displacement $x$	Angular displacement $\theta$
Velocity $v$	Angular velocity $\omega$
Acceleration $a$	Angular acceleration $\alpha$
Mass $m$	Moment of inertia $I$
Force $F$	Torque $\tau$
Newton's 2nd law: $F = ma$	$\tau = I\alpha$
Kinetic energy: $\frac{1}{2}mv^2$	$\frac{1}{2}I\omega^2$
Momentum: $p = mv$	Angular momentum: $L = I\omega$

Q.Write down the formula for work done in rotatory motion.

Concept understanding — Rotational Dynamics

Rotational Dynamics: The Physics of Spinning Things

The Core Idea

Breaking It Down

Torque — The Rotational "Push"

Moment of Inertia — The Rotational "Mass"

Angular Acceleration — How Fast Rotation Changes

The Complete Picture: Rotational Analogues

The Key Insight: Conservation of Angular Momentum

Q.Write down the formula for work done in rotatory motion.

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