Circular Motion formulas

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

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Formulas: 32
Subject: Physics
Exam: JEE Advanced
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Circular Motion, every formula

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

Arc–angle relation
$s = r θ$
Angular velocity
$ω = \frac{d θ}{d t}$
Angular acceleration
$α = \frac{d ω}{d t}$
Speed–angular velocity
$v = r ω$
Centripetal acceleration
$a_{c} = \frac{v ^{2}}{r} = ω^{2} r$
Tangential acceleration
$a_{t} = \frac{d v}{d t} = r α$
Total acceleration
$a = a_{c}^{2} + a_{t}^{2}$
Centripetal force
$F_{c} = \frac{m v ^{2}}{r} = m ω^{2} r$
Time period
$T = \frac{2 π}{ω} = \frac{2 π r}{v}$
Angular kinematics (1)
$ω = ω_{0} + α t$
Angular kinematics (2)
$θ = ω_{0} t + \frac{1}{2} α t^{2}$
Angular kinematics (3)
$ω^{2} = ω_{0}^{2} + 2 α θ$
Conical pendulum tension
$T cos θ = m g, T sin θ = m ω^{2} r$
Conical pendulum period
$T_{p} = 2 π \frac{L cos θ}{g}$
Bending of a cyclist
$tan θ = \frac{v ^{2}}{r g}$
Banking without friction
$tan θ = \frac{v ^{2}}{r g}$
Banking with friction (max)
$v_{m a x} = \frac{r g ( μ + tan θ )}{1 - μ tan θ}$
Skidding on a level road
$v \leq μ r g$
Skidding on rotating platform
$ω_{m a x} = \frac{μg}{r}$
Concave bridge normal force
$N = m g cos θ + \frac{m v ^{2}}{r}$
Convex bridge normal force
$N = m g cos θ - \frac{m v ^{2}}{r}$
Vertical circle: min speed at top
$v_{t o p} = g L$
Vertical circle: min speed at bottom
$v_{b o tt o m} = 5 g L$
Vertical circle: oscillation condition
$u \leq 2 g L$
Tension at any point (vertical circle)
$T - m g cos θ = \frac{m v ^{2}}{L}$
Tension at bottom (min looping)
$T_{b o tt o m} = 6 m g$
Death well / rotor minimum speed
$v_{m i n} = \frac{g r}{μ}$
Centrifugal (pseudo) force
$f = m ω^{2} r (outward)$
Radius of curvature
$R = \frac{v ^{2}}{a _{⊥}}$
Effect of Earth's rotation
$N = m g - m R ω^{2} cos^{2} λ$
λ = latitude
Frequency
$f = \frac{1}{T} = \frac{ω}{2 π}$
Non-uniform: speed changes
$a_{t} \neq = 0 \Rightarrow speed varies$

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Circular Motion formulas

Circular Motion, every formula

Arc–angle relation

Angular velocity

Angular acceleration

Speed–angular velocity

Centripetal acceleration

Tangential acceleration

Total acceleration

Centripetal force

Time period

Angular kinematics (1)

Angular kinematics (2)

Angular kinematics (3)

Conical pendulum tension

Conical pendulum period

Bending of a cyclist

Banking without friction

Banking with friction (max)

Skidding on a level road

Skidding on rotating platform

Concave bridge normal force

Convex bridge normal force

Vertical circle: min speed at top

Vertical circle: min speed at bottom

Vertical circle: oscillation condition

Tension at any point (vertical circle)

Tension at bottom (min looping)

Death well / rotor minimum speed

Centrifugal (pseudo) force

Radius of curvature

Effect of Earth's rotation

Frequency

Non-uniform: speed changes

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