Question

A particle of mass 5kg is moving with a uniform speed ${\text{3}}\sqrt {\text{2}} {\text{cm/s}}$ in X-Y plane along the line $Y = X + 4$. The magnitude of its angular momentum about the origin in ($g\, cm^2/s$) is (x and y are in cm).

Answer 1

In this problem,we are going to apply the concept of angular momentum (L).It is defined as the distance of the object from a rotation axis multiplied by the linear momentum.
$L{\text{ }} = {\text{ }}r{\text{ }} \times {\text{ }}p{\text{ }}or{\text{ }}L{\text{ }} = {\text{ }}m{\text{ }} \times v{\text{ }} \times {\text{ }}r.\;$

Complete step by step answer:
Given: $m$= mass of particle= $5$
$V$= speed of particle in X -Y plane along with the line $\;y = x + 4.$
Angular momentum is the property of any rotating object given by moment of inertia times angular velocity. Angular momentum (L) is defined as the distance of the object from a rotation axis multiplied by the linear momentum.

{\text{ }}L{\text{ }} = {\text{ }}m{\text{ }} \times v{\text{ }} \times {\text{ }}r$$. Where $$r$$ = radius made by particle while moving along with line $p$ = linear momentum $m$ = mass of the particle $v$ = velocity with which particle is moving Angular momentum is a vector quantity. The line in X-Y plane along which a particle is moving can be written in the form: $$x - y + 4 = 0$$ Perpendicular distance from origin $$ = {\text{ }}4/\surd 2$$ Perpendicular distance from origin $$ = {\text{ }}2\surd 2$$ Now the angular momentum $$\left( L \right){\text{ }} = {\text{ }}m{\text{ }} \times v{\text{ }} \times {\text{ }}r$$ $$\left( L \right){\text{ }} = {\text{ }}5 \times 3\surd 2 \times 2\surd 2\;\;$$ $$\therefore\left( L \right) = 60\;{\text{ }}kg - {m^2}/s$$ **Therefore, the magnitude of its angular momentum about the origin is 60 units.** **Note:** The direction of the angular momentum comes from the right-hand rule, and will be in the same direction as the angular velocity and for a system of particles the total angular momentum of the system is the sum of the angular momenta of the particles.