2. Circular Motion
β’ βMotion of bodies in circular path is called circular motion.β
β’ During uniform circular motion, the direction of position
vector changes continuously but the magnitude remains
constant which is equal to r (radius of circular path)
β’ Speed and kinetic energy remain constant in circular
3. β’ βThe angle traced at the center of the circle by position vector in certain
time is called angular displacement.β
β’ Its direction is along axis of rotation and can be determined
by right hand rule
β’ SI unit is radian and Non S.I units are βdegreeβ and βrevβ.
β’ 1 cycle = 1rev = 1rotation = 2ο° rad = 360Β°
β’ 1Β° =
π
180
rad = 0.0174 rad 1 rad =
180Β°
π
= 57.3ΒΊ
β’ Angle swept by a minute hand in one complete rotation
is 3600.
β’ Angle swept by minute hand in one minute is 6o.
β’ Angle swept by minute hand in 5 minutes is 5 x 6o = 30o
ANGULAR DISPLACEMENT
4. β’ βRate of change of angular displacement is called angular
velocity.β
β’ πππ£ =
π₯π
π₯π‘
,
β’ ππππ = πππ
π₯π‘β0
π₯π
π₯π‘
β’ Its S.I unit rad sβ1. and Non S.I units are βdegree s-1β and
βrev s-1β .
ANGULAR VELOCITY
5. Angular speed of seconds, minute and hours hand of a
clock in rad s-1
β’ Second hand:
ο· =
π₯π
π₯π‘
=
2π
60
=
π
30
πππ π β1
β’ Minute hand:
ο· =
π₯π
π₯π‘
=
2π
60
=
π
30
πππ πππβ1
β’ Hour hand:
ο· =
π₯π
π₯π‘
=
2π
12
=
π
6
πππ ββ1
6. β’ The rate of change of angular velocity is defined as
angular acceleration.
β’ πΌ =
π2βπ1
π‘2βπ‘1
β’ πΌπππ = πππ
π₯π‘β0
π₯π
π₯π‘
β’ Unit: rad/sec2
β’ Its direction is along the axis of rotation
ANGULAR ACCELERATION
7. β’ If angular velocity increases, then πandπΌ are in same direction and
if angular velocity decreases, then π and πΌ are in opposite
direction
8. β’ s = rο ο±
β’ Vector form is given by π = π Γ π
β’ v = rο·
β’ Vector form is given by π£ = π Γ π
β’ a = rο‘
β’ π = πΌ Γ π
RELATION BETWEEN LINEAR AND ANGULAR
VARIABLES
9. βThe force required to bend a straight-line path of a body into the circular path is called
centripetal force.β
In vector form, centripetal force and acceleration can be written as;
πΉπ =
ππ£2
π
= πππ2 =
4π2
ππ
π2
= 4π2πππ2
πΉπ = β
ππ£2
π
π = β
ππ£2
π2
π β πππ2
π = ββ
πππ2
ππ =
π£2
π
= ππ2
= π
4π2
π2
= 4π2
π2
π
ππ = π£π
ππ = β
π£2
π
π = β
π£2
π2
π = βππ2π = βππ2
CENTRIPETAL FORCE (CENTRIPETAL
ACCELERATION)
11. β’ Work done by centripetal force is zero.
β’ Centripetal and centrifugal forces form true action & reaction pair
but they canβt balance each other because they donβt act on same
body.
12. A stone of mass 250 g is tied to the end of a string of length
1.0 m. It is whirled in a horizontal circle with a frequency of
30 rev./min. What is the tension in the string?
(a)
π2
4
π
(b)
π2
2
π
(c) π2
π
(d) 2Ο2
π
QUESTION-1
13. The ratio of angular speeds of minute hand and hour hand
of a watch is
(a) 6 : 1
(b) 12 : 1
(c) 1 : 12
(d) 1 : 6
QUESTION-2
14. The angular speed of a fly wheel making 120
revolutions/minute is
(a) 2Ο rad/s
(b) 4Ο2rad/s
(c) 4Ο rad/s
(d) Ο rad/s
QUESTION-3
15. Two cars of masses m1 and m2 are moving in circle of
radius r1 and r2. Their speeds are such that period of
rotation same. The ratio of their centripetal force is
(a) m1:m2
(b) r1:r2
(c) 1:1
(d) m1 r1:m2 r2
QUESTION-4
16. Angle between centripetal acceleration and radius vector
is
(a) 90o
(b) 180o
(c) 0o
(d) 45o
QUESTION-5
17. A particle on the rim of wheel covers distance of 0.3 m
when it turns angle of 30Β° find radius.
(a)
1.8
π
(b)
π
1.8
(c)
π
6
(d)
6
π
QUESTION-6
18. If a cycle wheel of radius 0.4m completes one revolution in
one second, then acceleration of the cycle is
(a) 0.4πππ β2
(b) 0.8πππ β2
(c) 0.4π2
ππ β2
(d) 1.6π2 π
π β2
QUESTION-7
19. The angle described in 2sec by an object rotating at a rate
of 600 rpm is
(a) 20ππππ
(b) 40ππππ
(c) 5ππππ
(d) zero
QUESTION-8