Question

A particle mass 1 kg is moving along a straight line y=x+4. Both x and y are in metres. Velocity of the particle is 2m//s. Find the magnitude of angular momentum of the particle about origin.

Answer 1

Given :

Mass of particle = m = 1 kg

The velocity of particle = v = 2 m/s²

A particle is moving along line  y = x + 4

To Find :

The magnitude of angular momentum of the particle about origin

Solution :

particle is moving along line  y = x + 4

The standard straight line equation = y = m x + c

Where m is the slope of line

Compare given line , we get ,

       Slope of straight line = tanФ = 1

Or,      Ф = $tan^{-1}$

∴         Ф = 45°

i.e  angle = 45°

And   displacement = d = 4  m

Now,

From momentum , P = mass × velocity

i.e        p = m v

As  momentum of the particle about origin

From figure

So, Taking momentum about  x-component

i.e        P = m v cosФ × d

Or,       P = 1 kg × 2 m/s² × cos 45° × 4 m

Or,       P =  1 kg × 2 m/s² × $\dfrac{1}{\sqrt{2} }$ × 4 m

∴       momentum = 4$\sqrt{2}$  kg m²/s²        

So, The magnitude of angular momentum of the particle about origin = P =  4$\sqrt{2}$  kg m²/s²

Hence,  The magnitude of angular momentum of the particle about origin is   4$\sqrt{2}$  kg m²/s²       Answer