Relation between Power (P), Torque (τ) and Angular velocity (ω) is:

(a) P = τ/ω
(b) P = τω
(c) P = ω/τ
(d) τ = Pω

Question

Relation between Power (P), Torque (τ) and Angular velocity (ω) is:

(a) P = τ/ω
(b) P = τω
(c) P = ω/τ
(d) τ = Pω

Accepted Answer

>

> [!TLDR]
> Just as linear power is force times velocity, rotational power is torque times angular velocity: $P = 	au\omega$.
>
> For rotational motion, the work done by a torque $	au$ in rotating a body through a small angle $d	heta$ is $dW = 	au\, d	heta$. Power is the rate of doing work:
> $$P = \frac{dW}{dt} = 	au\frac{d	heta}{dt} = 	au\omega$$ …

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.Relation between Power (P), Torque (τ) and Angular velocity (ω) is:

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.Relation between Power (P), Torque (τ) and Angular velocity (ω) is:

🎓Unlock everything free for 14 days

Unlock everything free for 14 days