Rotation formulas

Every formula JEE Advanced expects you to know for Rotation, with the variables spelled out. Free, no sign-up. Read it before a mock, not during one.

Practise these formulas 541 practice questions

Formulas: 32
Subject: Physics
Exam: JEE Advanced
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Rotation, every formula

32 formulas, typeset and free. Print it, or keep it open beside your practice.

MOI of a particle
$I = m r^{2}$
MOI of a system
$I = \sum m_{i} r_{i}^{2}$
Perpendicular axis theorem
$I_{z} = I_{x} + I_{y}$
plane lamina
Parallel axis theorem
$I = I_{c m} + M d^{2}$
Radius of gyration
$I = M K^{2}$
Solid sphere
$I = \frac{2}{5} M R^{2}$
Hollow sphere
$I = \frac{2}{3} M R^{2}$
Ring about its axis
$I = M R^{2}$
Disc about its axis
$I = \frac{1}{2} M R^{2}$
Solid cylinder
$I = \frac{1}{2} M R^{2}$
Rod about its centre
$I = \frac{M L ^{2}}{12}$
Rod about its end
$I = \frac{M L ^{2}}{3}$
Rectangular plate
$I = \frac{M ( a ^{2} + b ^{2} )}{12}$
Torque
$τ = r \times F, τ = r F sin θ$
Rotational Newton's law
$τ = I α$
Angular momentum
$L = r \times p = I ω$
Torque–angular momentum
$τ = \frac{d L}{d t}$
Conservation of angular momentum
$I_{1} ω_{1} = I_{2} ω_{2}$
τ_ext=0
Rotational kinetic energy
$K = \frac{1}{2} I ω^{2}$
Work by a torque
$W = τ θ$
Rotational power
$P = τ ω$
Angular impulse
$J = \int τ d t = Δ L$
Pure rolling condition
$v = R ω$
KE of a rolling body
$E = \frac{1}{2} m v^{2} (1 + \frac{K ^{2}}{R ^{2}})$
Acceleration down an incline
$a = \frac{g sin θ}{1 + \frac{K ^{2}}{R ^{2}}}$
Speed at the bottom of an incline
$v = \frac{2 g h}{1 + \frac{K ^{2}}{R ^{2}}}$
Rolling race order
$v_{s p h er e} > v_{d i sc} > v_{h o l l o w} > v_{r in g}$
Speed of the top of a rolling wheel
$v_{t o p} = 2 v$
Speed of a rim point
$v = 2 v_{c m} cos \frac{θ}{2}$
Friction for rolling on an incline
$f = \frac{m g sin θ}{1 + \frac{R ^{2}}{K ^{2}}}$
Combined kinetic energy
$E = \frac{1}{2} M v_{c m}^{2} + \frac{1}{2} I_{c m} ω^{2}$
Rotational equilibrium
$\sum τ = 0$

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Rotation formulas

Rotation, every formula

MOI of a particle

MOI of a system

Perpendicular axis theorem

Parallel axis theorem

Radius of gyration

Solid sphere

Hollow sphere

Ring about its axis

Disc about its axis

Solid cylinder

Rod about its centre

Rod about its end

Rectangular plate

Torque

Rotational Newton's law

Angular momentum

Torque–angular momentum

Conservation of angular momentum

Rotational kinetic energy

Work by a torque

Rotational power

Angular impulse

Pure rolling condition

KE of a rolling body

Acceleration down an incline

Speed at the bottom of an incline

Rolling race order

Speed of the top of a rolling wheel

Speed of a rim point

Friction for rolling on an incline

Combined kinetic energy

Rotational equilibrium

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