First slide

Angular momentum

Question

A particle of mass m = 5 units is moving with a uniform speed $v = 3 \sqrt{2}$ , units in the XOY plane along the line y = x + 4. The magnitude of the angular momentum of the Particle about the origin is

Moderate

A

60 units
B

40 units
C

zero
D

10 units

Solution

Momentum of the particle,
$mV = 5 \times (3 \sqrt{2}) = 15 \sqrt{2}$
The direction of momentum in XOY plane is given by
y=x+4
The slope of the line is
$1 = \tan θ or θ = 45^{\circ}$
Intercept of the line =4
Length of the perpendicular z from the origin on straight line = 4sin 45°
$4 / \sqrt{2} = 2 \sqrt{2}$
$∴$ Angular momentum = (m v) x z
$= (15 \sqrt{2}) \times (2 \sqrt{2}) = 60 units$

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