Study Notes Circular Motion | Physics |Quick Revision| 11th Grade | 2025/26

CIRCULAR MOTION
Motion along a circular path : when a body is moving along a circular path with constant speed called uniform
circular motion, when speed is not constant, motion is said to be non-uniform circular motion.
 mv2 n̂ v
v
Fc 
r
 r ; ˆr  unit vector along radially outward
ˆ

A force required to keep of body on circular path always acts in radially
mv2 ˆr
O
inward direction called centripetal force whose magnitude is . FC
r
For non-uniform circular motion v
v
F  Fc rˆ  Ft nˆ 
Ft
n = unit vector along direction of motion or velocity
v
mv2 dv
Fc  and Ft  m. O F
r dt C


a  Resultan t or net acceleration  a rˆ  a nˆ
v dv a dv
 rˆ  nˆ  dt
r dt
2 2
 v2   dv 
O v2
r

 dv/ dt 
  tan1  2 
 v /r 
Angle of banking: Angle by which an outer edge of circular track is raised to provide the necessary centripetal
force through the horizontal component of normal reaction.

1  v 
2

angle of banking   tan  
 rg 
Motion of vehicle on a horizontal circular track:
mv2
is being provided by force of static friction i.e., Fs  us N and N=mg  v2  us rg or v 
r
Condition for no skidding on circular track
mv2 mv2 A
Fs  or us mg  or v 
r r N
Angle of bending of a cyclist on a rough horizontal circular
track to move on is given O B
Fs
1  v 
2 2
tan   v    tan  
rg  rg 