Solution of Mechanics - Part 2. Lesson 9th to 13th

82 Pages·2013·24.61 MB·English

Solutions
of

Mechanics Part-II
Lesson 9th to 13th

By DC Pandey

Mechanics of Rotational
Motion

= Introductory Exercise 9.1
1, The mass distribution is at minimum
separation from the diagonal passing
‘through entre to opposite corners ofthe
tube, 0, moment of inertia fe minimum
Shout that ai.

mi
ae

while Ly = mr? =:

(oy = 2 +22? + mat)
Mechanics of Rotational Motion | 9
6. 10. ‘The disk with smaller dengity will have
larger radius and as T=3 67, eo the

‘isk with larger radius will have higher
‘moment of inertia,

= Introductory Exercise 9.2
1. of =of +200

10

8. a(x 49? +2548" 43% 47? =5Nm

ft A)

+ 50% 08 + (100% 50" +99 49% + 08
488 4 BI)

= 100% 50" + 100% 494 +... + 100%

= 100018 +28 +3? +... +50")

00 50160 + D400 + D

6
50% 51% 100% 101,
4: | Mechanics-2

6 a. Lom@xd-mGisy)

x (00s 45°i + vsin 45°5)

=f 2x19 dt =10%#
tot
Mechanics of Rotational Motion | §

5. It depends upon the distance, velocity 4
‘and angle from the axis, which may not
‘ven zero from a different point.
= Introductory Exercise 9.4
1 u

sin
ae, = Introductory Exercise 9.6
" 2
6 | Mechanics-2

3.

fs
‘As the torque due to applied force is
‘anti-clockwise, so the point of contact
‘tos to slip rightwards and fiction tries
‘tw provent it and so acts lftwards

As during rolling down, friction acts
‘upward which exerts a torque, thus the
‘angular momentum ofthe system is not
‘conserved. Even if we take axis of
rotation at point of contact, then
‘component of weight exerts torque, 80,
statement is false

‘Force of fretion wil be zero, only when
Mechanics of Rotational Motion | 7

tan 0>y
‘And for toppling,
img sin 05 > mg cos 0%
tan 0>1
(@) Cube will slide before toppling sf
tan 0<l, Ley <land

(©) Cube will topple before sliding if
tan 0>1,4e,h>1

2 :
F20
ie, oven a lightest amount of fore can
Iniate motion af the dk
4 Accleration of point of contact is zoo
Gy when thers unforn pure rolling
ind no alipping
= Introductory Exercise 9.8 foruonta pane,f =O
L “ Impulse, I,
‘Angular Impulse,
For shiding
ing sin 0 > mg con 9
AIEEE Corner
= Subjective Questions (Level 1) 2. 1=1, +1,

1.

= 1G? +24) 4268 +48
8 | Mechanics-2

4 wey

10. 1

T=myl + myt
Substituting the values we get,
mim) 2
im +m,

dl =dmx? = 24), de =3* (ax +P) de
at? + fa?) de
Jia +82) ae

Lye ge
roid

8. In socond!s clock, it takes 60 s by the
‘seconds hand to rotate by 2m.

Evade,
0
2.608 60° x 01 - 10 0.25 -9% 0.25
19 _24-19 166 _ 83

05-12 188 83 Nm
20
1 29 _ 2x 50x28
at =p q = 28 2850038
2 ee
=Bnradle?
Srrad/s® x 5s ~40radle
1B. 0-0, +0, +05
aff tam tat,

of
hy (f, +) =2x56+2=70rad

2

20. ona, +t
= -20rads
20 rad/s —2rad/s* x t
pa)
7

(As KE= Lio! is same foro)

monat-tat
Ro} 1 4ug 9R° ad,
“4ug 2° BR 167g?
ahahaha

Cr

28. @t-Te and 0-05 ot
art