Question

A particle of mass 5 kg is moving with a uniform speed 3√2 in XOY plane along the line Y= X + 4 the magnitude of its angular momentum about the origin is

Answer 1

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Answer 2

Given:

• Mass = 5 kg
• Speed = 3√2 m/s
• Line equation : y = x + 4

To find:

• Angular momentum about origin ?

Calculation:

The equation is :

y = x + 4

=> x - y + 4 = 0

• First of all, latest calculate the perpendicular distance of origin from the line :

$r_{ \perp} = \dfrac{0 - 0 + 4}{ \sqrt{ {1}^{2} + {1}^{2} } }$

$\implies r_{ \perp} = \dfrac{4}{ \sqrt{ 2 } }$

$\implies r_{ \perp} =2 \sqrt{2} \: m$

Now, the angular momentum will be :

$\implies L = m \times v \times r_{ \perp}$

$\implies L = 5 \times 3 \sqrt{2} \times 2 \sqrt{2}$

$\implies L = 60 \: kg \: {m}^{2} /s$

So, angular momentum w.r.t origin is 60 kgm²/s.