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1. REVIEW LECTURE-3
UNIT-3
(ROTATIONAL & CIRCULAR
MOTION)
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2. Circular Motion
• “Motion of bodies in circular path is called circular motion.”
• 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)
• Speed and kinetic energy remain constant in circular

3. • “The angle traced at the center of the circle by position vector in certain
time is called angular displacement.”
• Its direction is along axis of rotation and can be determined
by right hand rule
• SI unit is radian and Non S.I units are “degree” and “rev”.
• 1 cycle = 1rev = 1rotation = 2 rad = 360°
• 1° =
𝜋
180
rad = 0.0174 rad 1 rad =
180°
𝜋
= 57.3º
• Angle swept by a minute hand in one complete rotation
is 3600.
• Angle swept by minute hand in one minute is 6o.
• Angle swept by minute hand in 5 minutes is 5 x 6o = 30o
ANGULAR DISPLACEMENT

4. • “Rate of change of angular displacement is called angular
velocity.”
• 𝜔𝑎𝑣 =
𝛥𝜃
𝛥𝑡
,
• 𝜔𝑖𝑛𝑠 = 𝑙𝑖𝑚
𝛥𝑡→0
𝛥𝜃
𝛥𝑡
• Its S.I unit rad s–1. and Non S.I units are “degree s-1” and
“rev s-1” .
ANGULAR VELOCITY

5. Angular speed of seconds, minute and hours hand of a
clock in rad s-1
• Second hand:
 =
𝛥𝜃
𝛥𝑡
=
2𝜋
60
=
𝜋
30
𝑟𝑎𝑑 𝑠−1
• Minute hand:
 =
𝛥𝜃
𝛥𝑡
=
2𝜋
60
=
𝜋
30
𝑟𝑎𝑑 𝑚𝑖𝑛−1
• Hour hand:
 =
𝛥𝜃
𝛥𝑡
=
2𝜋
12
=
𝜋
6
𝑟𝑎𝑑 ℎ−1

6. • The rate of change of angular velocity is defined as
angular acceleration.
• 𝛼 =
𝜔2−𝜔1
𝑡2−𝑡1
• 𝛼𝑖𝑛𝑠 = 𝑙𝑖𝑚
𝛥𝑡→0
𝛥𝜔
𝛥𝑡
• Unit: rad/sec2
• Its direction is along the axis of rotation
ANGULAR ACCELERATION

7. • If angular velocity increases, then 𝜔and𝛼 are in same direction and
if angular velocity decreases, then 𝜔 and 𝛼 are in opposite
direction

8. • s = r
• Vector form is given by 𝑆 = 𝜃 × 𝑟
• v = r
• Vector form is given by 𝑣 = 𝜔 × 𝑟
• a = r
• 𝑎 = 𝛼 × 𝑟
RELATION BETWEEN LINEAR AND ANGULAR
VARIABLES

9. “The force required to bend a straight-line path of a body into the circular path is called
centripetal force.”
In vector form, centripetal force and acceleration can be written as;
𝐹𝑐 =
𝑚𝑣2
𝑟
= 𝑚𝑟𝜔2 =
4𝜋2
𝑚𝑟
𝑇2
= 4𝜋2𝑚𝑟𝑓2
𝐹𝑐 = −
𝑚𝑣2
𝑟
𝑟 = −
𝑚𝑣2
𝑟2
𝑟 − 𝑚𝑟𝜔2
𝑟 = −​
𝑚𝑟𝜔2
𝑎𝑐 =
𝑣2
𝑟
= 𝑟𝜔2
= 𝑟
4𝜋2
𝑇2
= 4𝜋2
𝑓2
𝑟
𝑎𝑐 = 𝑣𝜔
𝑎𝑐 = −
𝑣2
𝑟
𝑟 = −
𝑣2
𝑟2
𝑟 = −𝑟𝜔2𝑟 = −𝑟𝜔2
CENTRIPETAL FORCE (CENTRIPETAL
ACCELERATION)

10. • Centripetal force in terms of K.E , Momentum and moment of
inertia.
• 𝐹𝑐 =
𝑚𝑣2
𝑟
×
2
2
=
1
2
𝑚𝑣2
2
𝑟
=
2𝐾. 𝐸
𝑟
• 𝐾. 𝐸 =
1
2
𝑝𝑣
• 𝐹𝑐 =
2𝐾. 𝐸
𝑟
= 2
1
2
𝑝𝑣
𝑟
=
𝑝𝑣
𝑟
• 𝐹𝑐 =
𝑚𝑣2
𝑟
=
𝑚𝑟2
𝜔2
𝑟
=
𝐼𝜔2
𝑟

11. • Work done by centripetal force is zero.
• Centripetal and centrifugal forces form true action & reaction pair
but they can’t balance each other because they don’t 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
𝑁
(b)
𝜋2
2
𝑁
(c) 𝜋2
𝑁
(d) 2π2
𝑁
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) 2π rad/s
(b) 4π2rad/s
(c) 4π rad/s
(d) π 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 30° 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) 0.4𝜋𝑚𝑠−2
(b) 0.8𝜋𝑚𝑠−2
(c) 0.4𝜋2
𝑚𝑠−2
(d) 1.6𝜋2 𝑚
𝑠−2
QUESTION-7

19. The angle described in 2sec by an object rotating at a rate
of 600 rpm is
(a) 20𝜋𝑟𝑎𝑑
(b) 40𝜋𝑟𝑎𝑑
(c) 5𝜋𝑟𝑎𝑑
(d) zero
QUESTION-8

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