Three small balls of masses 1 k g , 2 k g and 3 k g are moving in a plane and their velocities are 1 m s - 1 , 2 m s - 1 and 3 m s - 1 , respectively as shown. The total angular momentum of the system

Question

Three small balls of masses 1 k g , 2 k g and 3 k g are moving in a plane and their velocities are 1 m s - 1 , 2 m s - 1 and 3 m s - 1 , respectively as shown. The total angular momentum of the system of three balls about point P at the given instant of time is

TestHub · Accepted Answer

The particle of mass 2 kg is situated perpendicular to the axis of rotation. So, the angle will be $90 °$ . Similarly, the particle of mass 1 kg is situated opposite side of the circular path. So, the angle will be $90 °$ and angular momentum will act in opposite direction.

According to the diagram, total angular momentum

$= 2 \times 2 \times 2 \sin 90 ° + 3 \times 3 \times 3 \sin 0 ° - 1 \times 1 \times 1 \sin 90 °$

$= 8 - 1$

$= 7 \frac{kg m^{2} s^{- 1}}{s}$ $[∵ \sin 0 ° = 0 a n d \sin 90 ° = 1]$

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