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.]

A particle of mass 50 gm moving in a circle at 5 cm radius with a cons

1.	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.]
Answer» Solution :`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.