JEE Physics›Mechanics›Formulas
Formula Sheet

Mechanics Formulas

All key formulas grouped by subtopic. Each one has a quick reminder and common mistakes to watch for.

15 formulas · 5 subtopics

Newton's Second Law

#1
F⃗net=ma⃗\vec{F}_{\text{net}} = m\vec{a}

💡 Always draw FBD first. Take components along and perpendicular to motion.

⚠ Forgetting pseudo forces in non-inertial frames.

Newton's Third Law

#2
F⃗AB=−F⃗BA\vec{F}_{AB} = -\vec{F}_{BA}

💡 Action-reaction pairs act on DIFFERENT bodies. Never put both on same FBD.

⚠ Treating normal force and weight as action-reaction pair (they act on the same body).

Friction Force

#3
fs≤μsN,fk=μkNf_s \leq \mu_s N, \quad f_k = \mu_k N

💡 Static friction adjusts up to maximum. Kinetic friction is constant.

⚠ Using f = \mu N for static friction when body is not on the verge of sliding.

Angle of Friction

#4
tan⁡λ=μs\tan \lambda = \mu_s

💡 Body slides on incline when inclination angle > angle of friction.

Centripetal Acceleration

#5
ac=v2r=ω2ra_c = \frac{v^2}{r} = \omega^2 r

💡 Always directed towards center. It is not a separate force.

⚠ Adding centripetal force as an extra force in FBD. It is the net radial force.

Banking of Roads

#6
tan⁡θ=v2rg(no friction)\tan \theta = \frac{v^2}{rg} \quad \text{(no friction)}

💡 With friction, the formula changes depending on whether the vehicle tends to slide up or down.

Work-Energy Theorem

#7
Wnet=ΔKE=12mv2−12mu2W_{\text{net}} = \Delta KE = \frac{1}{2}mv^2 - \frac{1}{2}mu^2

💡 Include work by ALL forces (gravity, friction, normal, applied).

⚠ Forgetting work done by friction or normal force on inclines.

Work Done by Variable Force

#8
W=∫x1x2F⃗⋅dx⃗W = \int_{x_1}^{x_2} \vec{F} \cdot d\vec{x}

💡 For spring: W = \frac{1}{2}kx^2. Sign depends on direction of force and displacement.

Conservation of Mechanical Energy

#9
KE1+PE1=KE2+PE2(when Wnc=0)KE_1 + PE_1 = KE_2 + PE_2 \quad \text{(when } W_{\text{nc}} = 0\text{)}

💡 Only valid when non-conservative forces do no work. Otherwise use W_{nc} = \Delta E.

⚠ Applying conservation of energy when friction is present.

Power

#10
P=dWdt=F⃗⋅v⃗P = \frac{dW}{dt} = \vec{F} \cdot \vec{v}

💡 Instantaneous power uses dot product. Average power = total work / total time.

Conservation of Linear Momentum

#11
m1v⃗1+m2v⃗2=m1u⃗1+m2u⃗2m_1 \vec{v}_1 + m_2 \vec{v}_2 = m_1 \vec{u}_1 + m_2 \vec{u}_2

💡 Always valid when net external force = 0. Works component-wise.

⚠ Applying momentum conservation when external forces (like friction) act during collision.

Coefficient of Restitution

#12
e=v2−v1u1−u2=relative speed of separationrelative speed of approache = \frac{v_2 - v_1}{u_1 - u_2} = \frac{\text{relative speed of separation}}{\text{relative speed of approach}}

💡 e = 1 (perfectly elastic), e = 0 (perfectly inelastic), 0 < e < 1 (inelastic).

⚠ Using e along the wrong direction in oblique collisions. e applies along line of impact only.

Head-on Elastic Collision Velocities

#13
v1=(m1−m2)u1+2m2u2m1+m2,v2=(m2−m1)u2+2m1u1m1+m2v_1 = \frac{(m_1 - m_2)u_1 + 2m_2 u_2}{m_1 + m_2}, \quad v_2 = \frac{(m_2 - m_1)u_2 + 2m_1 u_1}{m_1 + m_2}

💡 Special case: equal masses exchange velocities. Heavy hitting light: light goes at ~2u.

Constraint Relations (Pulley Systems)

#14
String length constant: ∑li=const  ⟹  ∑l˙i=0\text{String length constant: } \sum l_i = \text{const} \implies \sum \dot{l}_i = 0

💡 Differentiate string length equation to get velocity and acceleration constraints.

⚠ Wrong sign convention when differentiating string constraints.

Vertical Circular Motion (String)

#15
vtop, min=gR,vbottom, min=5gRv_{\text{top, min}} = \sqrt{gR}, \quad v_{\text{bottom, min}} = \sqrt{5gR}

💡 At top: T + mg = mv^2/R. Minimum speed when T = 0.

⚠ Using same formula for rod (where minimum speed at top = 0) as for string.
Next
Electrostatics & Capacitors
→