# MHT-CET Physics Crash Course “Angular Momentum and its Expression” Class 12

## “Angular Momentum and its Expression” MHT-CET Class 12 Physics Crash Course| Chapter Rotational Dynamics

In this session G.S. Khairnar discussed the theory and MCQ’s of “Angular Momentum and its Expression”. The session will be useful for all the aspirants of MHT-CET 2022. The session will be in Marathi and English.

### Angular Momentum and its Expression:-

Dear students, we know that in linear motion, mass is the factor which provides the inertia. In linear motion, product of mass and velocity of object gives rise to linear momentum given as,

p=mv

Inertia in rotational motion is provided by moment of inertia, which is the product of mass of particle and square of its perpendicular distance from the axis of rotation. So that the mass in linear is replaced by moment of inertia in rotational motion.

As per the physical significance of moment of inertia, the linear momentum in translational motion is also replaced by angular momentum which is define as,

“Angular momentum of rotating body is defined as the product of linear momentum of particle and the perpendicular distance of the particle from axis of rotation”.

Let’s derive the expression for angular momentum in rotational motion……!

Consider a body consists ‘n’ number of particles of masses m1, m2,…….mn situated at distances r1, r2 …rn respectively from the axis of rotation passing through point ‘O’ is rotating with constant angular velocity ‘ω’. The particle of mass m1 having linear velocity v1 = r

The linear momentum is,

P1 = m1v1

P1 = m1r1

The angular momentum i.e. moment of linear momentum is product of linear momentum.

L1= P1r1

L1= m1rr1

L1 = m1r12ω

Similarly, for remaining particles we can write,

∴ L2 = m2r22ω

∴  Ln =  mnrn2ω

The sum of angular momentum of particle is called angular momentum of body.

L = L1 + L2 + ………….. + Ln

This is an expression for the angular momentum of rotating body.

Thus angular momentum of a body is equal to the product of M.I. of body & its angular velocity.

S.I. unit is Kg.m2/s and its CGS unit is g.cm2/s.

Its dimensions are [L] = [M1L2T-1]

Points to remember:

Conservation of angular momentum:

Statement: If no external torque acts on rotating body, the angular momentum of the body remains constant.

Proof: The relation between torque & angular acceleration is

τ = I α
Where I is M.I. of the body.

But the definition of angular acceleration

[Torque is rate of angular momentum. As force is rate of change of momentum].

If no external torque acts on body then

### Angular Momentum and its Expression

Let’s solve some MCQ’s….!

Q.1) Angular momentum of rotating body in vector form is given as,

Q.2) Which of the following is unit of angular momentum?

a) m2/ s2

b) m/s

c) s2/m

d) m2/s

d) m2/s

Q.3) The dimensions of angular momentum are…

a) [M2L2T-1]

b) [M1L2T-1]

c) [M1L-1T-1]

d) [M1L2T-2]

b) [M1L2T-1]

Q.4) Which among the following is correct expression for angular momentum….…

Q.5) A disc of mass 0.2 kg and radius 6 cm rotating about its centre at the rate of 120 rpm, angular momentum of disc is…

Q.6) Uniform rod of mass 200 g and length 80 cm rotating at about its end perpendicular to length at the rate of 2π rad/s. Angular momentum of rod is…

Q.7) Angular momentum of rod when its moment of inertia and angular frequency becomes half of the initial value is…

Q.8) Ratio of angular momentum of rod rotating about an axis passing through its centre at 2 rps to the about an axis passing through its one end at 3 rps is…

a) 1:2

b) 2:1

c) 1:6

d) 6:1

c) 1:6

### ♦जिल्हा नुसार जाहिराती ♦

अहमदनगर अकोला अमरावती औरंगाबाद भंडारा बुलढाणा
चंद्रपुर धुले गढ़चिरौली गोंदिया हिंगोली जलगांव
जालना कोल्हापुर लातूर मुंबई नागपुर नांदेड़
नंदुरबार नाशिक उस्मानाबाद पालघर परभानी पुणे
रायगढ़ रत्नागिरि सांगली सातारा सिंधुदुर्ग सोलापुर
ठाणे वर्धा वाशिम यवतमाल बीड

### ♦शिक्षणानुसार जाहिराती ♦

७ वी (7th) दहावी (SSC) बारावी (HSC) डिप्लोमा आय.टी.आय पदवी
पदव्युत्तर शिक्षण बी.एड एम.एड एल.एल.बी / एल.एल.एम बीएससी एमबीए
बीसीए एमसीए बी.कॉम एम.कॉम GNM/ANM एमएससी
बी.फार्म एम.फार्म बी.ई एम.ई BAMS/BHMS एम.बी.बी.एस / एम.डी
बी.टेक एम.टेक MS-CIT