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

Option (d)

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

Step-by-step 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