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Friction formula sheet

Every formula in the Friction chapter for JEE Main, with one line on when it applies. Topic 1 is open to everyone; sign in free to read all 26 and download the PDF.

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How we count: 7× asked means 7 past JEE Main questions in the PrepWiser bank needed that formula, and "last" is the latest year one appeared. ★ marks formulas asked 8 or more times.

Static and kinetic friction

Static and limiting friction
7× asked, last 2023
0≤fs≤fmax⁡=μsN0\le f_s\le f_{\max}=\mu_sN
Static friction is whatever stops slip, up to μsN\mu_sN. "Just about to move": f=μsNf=\mu_sN.
Kinetic friction
7× asked, last 2024
fk=μkN,μk<μsf_k=\mu_kN,\qquad \mu_k<\mu_s
Once sliding; nearly independent of speed. Neither depends on the area of contact.
Push growing with time
F=kt ⇒ t0=μsmgkF=kt\ \Rightarrow\ t_0=\frac{\mu_smg}{k}
Friction equals FF (a 45∘45^\circ line) up to μsN\mu_sN, then drops to μkN\mu_kN.
Sliding to rest on level ground
4× asked, last 2023
a=μkg,s=u22μkg,t=uμkga=\mu_kg,\qquad s=\frac{u^2}{2\mu_kg},\qquad t=\frac{u}{\mu_kg}
Only friction acts along the floor, so mass cancels; aa = retardation.
Bag dropped on a moving belt
t=vμg,sground=sslip=v22μgt=\frac{v}{\mu g},\qquad s_{\text{ground}}=s_{\text{slip}}=\frac{v^2}{2\mu g}
Belt speed vv; friction speeds the bag up at μg\mu g until it reaches vv.
Work against friction
3× asked, last 2024
Wf=μkNdW_f=\mu_kNd
N=mgN=mg level, mgcos⁡θmg\cos\theta on an incline. Rest to rest: PE lost =μkN×=\mu_kN\times rough length only.
Rolling vs sliding
1× asked, last 2021
frolling≪fk<fmax⁡f_{\text{rolling}}\ll f_k<f_{\max}
Rolling without slipping needs only static friction, which does no work on a fixed surface.

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Practise Friction

19 more formulas in 4 topics

Angle of friction and angle of repose; Forces at an angle, walls and minimum force; Motion on a rough incline; and Two blocks, accelerating frames and chains. Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Angle of friction and angle of repose

  • Angle of friction2×
  • Angle of repose5×
  • Constant velocity on an incline
  • Resting on a curved surface3×

Forces at an angle, walls and minimum force

  • Pulling or pushing at an angle3×
  • Force to just start motion2×
  • Minimum force to move a block1×
  • Block pressed against a wall2×
  • Sliding or toppling1×

Motion on a rough incline

  • Sliding down a rough incline7×
  • Moving up a rough incline2×
  • Up and back over the same distance2×
  • Rough vs smooth: time ratio3×
  • Push up or hold (force along the incline)3×

Two blocks, accelerating frames and chains

  • Two blocks: together or slipping3×
  • Two blocks, rough floor
  • Block slid onto a plank
  • Box on an accelerating truck
  • Chain hanging off a rough table1×

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