Question

A particle of mass 2 kg is on a smooth horizontal table and moves in a circular path of radius 0.6m. The height of the table from the ground is 0.8m If the angular speed of the particle is $12rad{s^{ - 1}}$, the magnitude of its angular momentum about a point on the ground right under the center of the circle is:
A) $8.64kg{m^2}{s^{ - 1}}$
B) $11.52kg{m^2}{s^{ - 1}}$
C) $14.4kg{m^2}{s^{ - 1}}$
D) $20.16kg{m^2}{s^{ - 1}}$

Answer 1

Hint: Angular momentum is defined as the measure of the rotational momentum of the rotating body which is equal to the product of the angular velocity of the system and the moment of the inertia to the axis. Angular momentum is a vector quantity.

Complete step by step solution:
Given data:
The mass of a particle = 2 kg
The radius of the particle = 0.6m
Height = 0.8m
The angular speed of the particle, $\omega = 12rad{s^{ - 1}}$
The angular momentum =?
The perpendicular distance between the point and mass ${r_ \perp }$ is given by,
\[{r_ \perp } = \sqrt {{{\left( {0.6} \right)}^2} + {{\left( {0.8} \right)}^2}} = 1m\]
We know that the angular momentum is given by the formula, $L = mvr$
$ \Rightarrow L = m\left( {r\omega } \right){r_ \perp}$
$ \Rightarrow L = 2 \times 12 \times 0.6 \times 1 = 14.4kg{m^2}{s^{ - 1}}$
$ \Rightarrow L = 14.4kg{m^2}{s^{ - 1}}$
Thus the angular momentum, $L = 14.4kg{m^2}{s^{ - 1}}$.

Hence the correct option is C.

Additional Information:
1. As the mass increases, the angular momentum also increases. Hence we can say that the mass will be directly proportional to the angular momentum.
2. Angular momentum also depends on the rotational velocity and the rotational inertia. Whenever the object changes its shape, the angular velocity changes, and thus the angular momentum also changes.
3. When the matter consists of more number of protons than electrons, then we can say that the electric charge is the positive charge. Similarly, when the matter consists of more electrons than protons, then we can say that the electric charge is the positive charge.

Note: 1. Momentum is defined as the product of the mass of the particle and its velocity. Momentum is a vector quantity and has both magnitude and direction. If the object’s velocity changes, the momentum also changes. Impulse is described as the effect of force acting over time to change the momentum of an object. It is expressed as J.
2. The changes in the angular momentum are equivalent to torque.
3. Jean Buridan who is the discoverer of momentum also discovered angular momentum.