physics. session rotational mechanics - 1 session opener earth rotates about its own axis in one...
TRANSCRIPT
Physics
Session
Rotational Mechanics - 1
Session Opener
Earth rotates about its own axis in one day. Have you ever wondered what will happen to the length of a day if all the sea-water was to evaporate?
Session Objectives
Session Objective
1. Definitions of Angular Velocity & Acceleration(Instantaneous/Average)
2. Rotational Kinematics Equations
3. Relation between angular and Linear Quantities
Angular Displacement
It is the angle turned by a body or particle about a given axis of rotation
It is dimensionless Unit: Radians
Angular velocity
2 1
av2 1
–
t – t t
t 0
dlim
t dt
Instantaneous angular Velocity
Average angular Velocity
Unit : rad/s
Angular acceleration
2 1
av2 1
–
t – t t
t 0
dlim
t dt
Instantaneous angular acceleration:
Average angular acceleration:
Unit : rad/s2
LINEAR ANGULAR
Displacement
Velocity
Acceleration
12 xxx 12
dt
dxv
dt
d
dt
dva
dt
d
Linear and Angular Variables
Ox
y
v
r
S
rs
dt
drv
P
ra t
dt
d
ra 2r
2r
2t aaa
at
ar
a
Relationship Between Angular and Linear quantities
Ox
y
00
1
1
O
a
x
y
t=0x=x0
v0
t=tx=x1
v1
Rotational Kinematics Equations
21 0 0
1x x v t at
2 2
1 0 01
t t2
a is constant
1 0v v at
2 21 0 1 0v v 2a x x 2 2
1 0 1 02
is constant
1 0 t
Class Test
Class Exercise - 1
The length of the seconds hand of a clock is 10 cm. The speed of the tip of the hand is
(a) cm/ s (b) cm/ s4 2
(c) cm/ s (d) cm/ s3 8
Solution :
2 2v r r 10 cm/s
T 60 3Hence Answer is (c)
Class Exercise - 2
A body of mass 100 g revolves in a circle on a horizontal frictionless table attached by a cord 21 cm long to a pin set on the surface. If the body makes 2 complete revolutions per second, find the force exerted on it by the chord.
(a) 3.23 N (b) 3.40 N(c) 3.38 N (d) 3.32 N
Solution :
2 2
= 4 rad/s, r = 0.21 m, m = 0.1 kg.
F = mr = (0.1)(0.21)(4 ) = 3.32 N
Hence Answer is (d)
Class Exercise - 3
A motor car is traveling at 30 m/s on a circular road of radius 500 m. It is increasing in speed at a rate of 2 m/s2. What is its acceleration?
v = 30 m/s, r = 500 m, at = 2 m/s
2 2
2r
v (30)a 1.8 m/s
r 500
2 2 2r ta a a 2.7 m/s
Solution :
Class Exercise - 4
A constant torque is acting on a wheel. If starting from rest the wheel makes n rotations in t seconds, the angular acceleration is given by:
2 2
4 n 4 t(a) (b)
t n4 n
(c) 4 nt (d)t
Solution
0 = 0, = 2 n, = ?
20
1t t
2
Hence answer is (a)
21or 2 n t
2
24 n
ort
Class Exercise - 5
We know,
2d 9t 2t
–dt 20 3
29 5 10– 7.92 rad/s
20 3at t = 5s
Solution :
Hence answer is (b)
3 29t 2t60 6
A particle starts rotating from rest
according to the formula .
The angular velocity at the end of 5 seconds is
(a) 7.8 rad/s (b) 7.92 rad/s
(c) 7.5 rad/s (d) 9.72 rad/s
3 29t 2t60 6
Class Exercise - 6
In the previous question the angular acceleration of the particle at the end of 5s will be
(a) 3.38 rad/s2 (b) 8.38 rad/s2
(c) 8.33 rad/s2 (d) 3.83 rad/s2
2d 18t 2
– 3.83 rad/sdt 20 3
Solution :
Hence answer is (d)
Class Exercise - 7
A flywheel rotating at the rate of 120 rpm slows down to rest at a constant rate of 2 rad/s2. How many rotations does it make in the process?
2(a) 2 rev (b) 4 rev
(c) 4 2 rev (d) 2 rev
Solution
Hence answer is (d)
1
22
= 120 rpm = 4 rad/s,
= 0, = -2 rad/s
2 22 1 = + 2(- )
2 21 216
or 42 4
24Number of rotations 2 .
2
Class Exercise - 8A flywheel is rotated at a speed of 60 rad/s. Because of friction on the axle, it comes to rest in 5 minutes. The angular retardation is
(a) 0.3 rad/s2 (b) 2 rad/s2
(c) 3 rad/s2 (d) 0.2 rad/s2
0 = 60 rad/s, = 0, t = 5 min = 300 s.
0 = + (- )t
0 260
or 0.2 rad/st 300
Solution :
Hence answer is (d)
Class Exercise - 9A wheel rotating at a speed of 600 rpm about its axis is brought to rest by applying a constant torque for 10 seconds. The angular velocity after 5 seconds is(a) rad/s (b) 2 rad/s
(c) 5 rad/s (d) 3 rad/s
Solution
Hence answer is (a)
0 = 60 rpm = 1 rps = 2 rad/s
= 0, t = 10 s
2
02
t or rad/s10 5
Angular velocity after 5 s is given by
0 (– )5
2 – 5 rad/s5
Class Exercise - 10
A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first 2 s, it rotates through an angle 1, in the next 2s it rotates through an angle 2. The
ratio of is2
1(a) 1 (b) 2
(c) 3 (d) 5
Solution
21
1(2) 2
2
Hence answer is (c)
21 2
1(4) 8
2
2or 8 – 2 6
2
1
63
2
Thank you