Question

Two particles of mass 1 kg each are attached to a massless rod a distance of 1 m and 2m respectively from the axis of rotation. The angular speed of the system is 1 rad/s.
What is the angular momentum of the system? (in SI units)

a) 1

b) 2

c) 3

d) 4

Answer 1

Answer:

Option (d)

The angular momentum of the system is 5 Kg-m²/s

Explanation:

Angular momentum: Angular momentum is the product of angular velocity and of moment of inertia.

Angular momentum is dented by L

And the unit of angular momentum is Kg-m²/s

L= I×ω  

I is momentum of inertia

ω is angular velocity.

The unit of angular velocity  is red/s.

Momentum of inertia : Momentum of inertia is the sum  square the perpendicular distance from the rotational axis to of product mass of each particle of the body.

$I=\sum Mr^2$

The S.I unit of momentum of inertia is kg-m²

The angular momentum of a system is:

L= ∑I ω

  =∑ Mr²ω      [ Since $I=\sum Mr^2$]

Given , M= 1 kg,  r₁=1 m , r₂= 2 m and   ω = 1 rad/s.

The angular momentum of the system is

L= Mr₁²ω+Mr₂²ω

  = Mω(r₁²+r₂²)

 = {1×1 (1²+2²)}

=5 Kg-m²/s