A particle of mass 50 gm moving in a circle at 5 cm radius with a constant speed of 10 cm/s. What is its angular momentum about (i) centre of the circle, (ii) a point on the axis of the circle at 4 cm distance from its centre ? Which of these will be always in the same direction ? [Fig.]

Explanation

`m=0.050 kg, r = 5cm = 0.05 m, v= 10 cm//s`
(i) Angular momentum about the centre of the circle
`L_(1) = mvr = 0.050 xx 0.1 xx 0.05`
`=2.5 xx 10^(-4) J.s`
The direction of `L_(1)` is perpendicular to the plane ofthe circle
(ii) Angular momentum about a point on the axis 4 cm distance from its centre `=L_(2)` = ?
OB = 4 cm, `BA = sqrt(4^(2) + 5^(2)) = 6.4 cm = 0.064 m`
`L_(2)=0.05 xx 0.1 xx 0.064`
`=3.2 xx 10^(-4) J.s`
`L_2` is perpendicular to the plane of its position vector `vec(OA)` and the instantaneous velocity of the particle. Direction of `L_2` changes with time. The direction of `L_(1)` remains constant.