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A particle is moving in a circular path of radius a, with a constant velocity $v$ as shown in the figure. The center of circle is marked by ‘C’. The angular momentum from the origin O can be written as :

Option 1)
$va(1+cos\, 2\theta )$

Option 2)
$va(1+cos\, \theta )$

Option 3)
$va \, cos\,2 \theta$

Option 4)
$va$

Answers (2)

best_answer

As we have learned

Angular momentum -

$\vec{L}=\vec{r}\times \vec{p}$

- wherein

$\vec{L}$ represent angular momentum of a moving particle about a point.

it can be calculated as $L=r_1\, P=r\, P_1$

$r_1$ = Length of perpendicular on line of motion

$P_1$ = component of momentum along perpendicualar to $r$

$\cos \theta = \frac{a^2 + L^2 -a^2 }{2aL}\: \: or\: \: L = 2a \cos \theta$

component of length $\perp ^r$ to velocity

$=L \cos \theta$

$=2a \cos ^2 \theta$

$\cos 2 \theta =2 \cos ^2 \theta -1$

$= 2 \cos ^2 \theta = 1+ \cos 2 \theta$

$L_\perp = a(1+ \cos 2 \theta )$

$Angular\ momentum L =mvL_\perp = mv a(1+ \cos 2\theta )$

Option 1)

$va(1+cos\, 2\theta )$

Option 2)

$va(1+cos\, \theta )$

Option 3)

$va \, cos\,2 \theta$

Option 4)

$va$

Posted by

SudhirSol

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Posted by

Hemam Mousmi devi

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