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Question
A particle moves on a straight line with a uniform velocity. Its angular momentum __________ .
(a) is always zero
(b) is zero about a point on the straight line
(c) is not zero about a point away from the straight line
(d) about any given point remains constant.
Solution
(b) is zero about a point on the straight line
(c) is not zero about a point away from the straight line
(d) about any given point remains constant
(b) Angular momentum = \[m\left( \overrightarrow{r} \times \overrightarrow{v} \right)\]
If the point is on the straight line, \[\overrightarrow{r} \text{ and } \overrightarrow{v}\] will have the same direction and their cross product will be zero. Hence, angular momentum is zero.
(c) If the point is not on the straight line, \[\overrightarrow{r} \text{ and } \overrightarrow{v}\] will not have the same direction and their cross product will not be zero. Hence, angular momentum is non-zero.
(d) No external torque is applied on the body; therefore, its angular momentum about any given point remains constant.
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