Short Notes: Momentum (Linear and Angular)

 Page 1


Momentum (Linear and Angular)
Moment of Inertia: Momentum of inertia can be defined as
r = distance of the body of mass, m from centre of asis. 
• Very thin circular loop (ring): l=MR2
Thin circular ring
where, M = mass of the body 
R = radius of the ring 
/ = moment of inertia
• Uniform circular loop
/ - E
m.r'
* J
Page 2


Momentum (Linear and Angular)
Moment of Inertia: Momentum of inertia can be defined as
r = distance of the body of mass, m from centre of asis. 
• Very thin circular loop (ring): l=MR2
Thin circular ring
where, M = mass of the body 
R = radius of the ring 
/ = moment of inertia
• Uniform circular loop
/ - E
m.r'
* J
Uniform circular loop
• Uniform solid cylinder
Uniform solid cylinder
• Uniform solid sphere 
/= -M R 1
5
Uniform solid sphere
• Uniform thin rod
(AA" ) moment of inertia about the centre and perpendicular axis to the rod moment 
of inertia about the one corner point and perpendicular (BB’) axis to the rod.
Very thin spherical shell
Page 3


Momentum (Linear and Angular)
Moment of Inertia: Momentum of inertia can be defined as
r = distance of the body of mass, m from centre of asis. 
• Very thin circular loop (ring): l=MR2
Thin circular ring
where, M = mass of the body 
R = radius of the ring 
/ = moment of inertia
• Uniform circular loop
/ - E
m.r'
* J
Uniform circular loop
• Uniform solid cylinder
Uniform solid cylinder
• Uniform solid sphere 
/= -M R 1
5
Uniform solid sphere
• Uniform thin rod
(AA" ) moment of inertia about the centre and perpendicular axis to the rod moment 
of inertia about the one corner point and perpendicular (BB’) axis to the rod.
Very thin spherical shell
Thin sperical shell
I = -M R 2 
3
• Thin circular sheet
4
A'
A’
Thin circular sheet
• Thin rectangular sheet
I
Thin rectangular sheet
• Uniform right cone
I = — MR2 
10
Uniform cone as a disc
Page 4


Momentum (Linear and Angular)
Moment of Inertia: Momentum of inertia can be defined as
r = distance of the body of mass, m from centre of asis. 
• Very thin circular loop (ring): l=MR2
Thin circular ring
where, M = mass of the body 
R = radius of the ring 
/ = moment of inertia
• Uniform circular loop
/ - E
m.r'
* J
Uniform circular loop
• Uniform solid cylinder
Uniform solid cylinder
• Uniform solid sphere 
/= -M R 1
5
Uniform solid sphere
• Uniform thin rod
(AA" ) moment of inertia about the centre and perpendicular axis to the rod moment 
of inertia about the one corner point and perpendicular (BB’) axis to the rod.
Very thin spherical shell
Thin sperical shell
I = -M R 2 
3
• Thin circular sheet
4
A'
A’
Thin circular sheet
• Thin rectangular sheet
I
Thin rectangular sheet
• Uniform right cone
I = — MR2 
10
Uniform cone as a disc
o
A part of uniform cone as a disc
Suppose the given section is 1/n th part of the disc, then mass of disc will be nM. 
Inertia of the disc,
= ^ W ) R 2
Inertia of the section,
T = 1 / =L\fR:
1 \* zuok I du< ‘L a -
Y l 2