Question 547: Centre of Mass and Rotational Motion

Question

A mass '$$M$$' is moving with constant velocity parallel to $$\mathrm{X}$$-axis. Its angular momentum with respect to the origin is

Accepted Answer

The angular momentum $$(\vec{L})$$ of a particle with respect to a point (in this case, the origin) is given by the cross product of the position vector $$(\vec{r})$$ and the linear momentum of the particle $$(\vec{p})$$, which is the product of the mass $$M$$ and its velocity $$\vec{v}$$:
$$\vec{L} = \vec{r} 	imes \vec{p}$$
If a mass $$M$$ is moving with constant velocity parallel to the X-axis, then its momentum $$\vec{p}$$ is also constant both in magnitude and direction, given by:
$$\vec{p} = M\vec{v}$$
where $$\vec{v}$$ is the constant velocity vector of the mass parallel to the X-axis.
The position vector $$\vec{r}$$ is a vector from the origin to the location of the mass M. Since the mass is moving with a constant velocity and not approaching or moving away from the origin, the perpendicular distance from the origin to the line of motion (essentially, the "arm" of the moment arm) remains constant.
The cross product of two vectors yields a vector that is perpendicular to the plane formed by the two original vectors and its magnitude is given by:
$$|\vec{L}| = |\vec{r}||\vec{p}|\sin{	heta}$$
where $$	heta$$ is the angle between $$\vec{r}$$ and $$\vec{p}$$.
Since the mass is moving parallel to the X-axis, the angle $$	heta$$ between the position vector from the origin and the momentum vector is constant, and so is the sine of that angle. Thus, the product $$|\vec{r}||\vec{p}|$$ is also constant.
Therefore, the magnitude of the angular momentum $$|\vec{L}|$$ is constant, and because the mass M is not changing its direction of motion or speed, the direction of the angular momentum vector is also constant.
The correct answer to the question is:
Option A: constant
since the angular momentum does not change with time when the velocity is constant and the direction of motion is a straight line, and because there are no external forces or torques acting on the mass to change its state of motion or angular momentum.

Answer

constant

Answer

zero

Answer

decreasing

Answer

increasing

Centre of Mass and Rotational Motion

A mass '$M' is moving with constant velocity parallel to \mathrm{X}$-axis. Its angular momentum with respect to the origin is

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