"Momentum and changes in momentum are not always in the same direction." Explain with a suitable example.

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(N/A) Consider a stone tied to a string being whirled in a horizontal circular path at a constant speed.
$1$. The momentum of the stone is given by $\vec{p} = m\vec{v}$. Since the speed is constant, the magnitude of momentum remains constant, but its direction is always tangential to the circular path and changes continuously.
$2$. The change in momentum $\Delta \vec{p}$ over a small time interval $\Delta t$ is given by $\Delta \vec{p} = \vec{p}_{final} - \vec{p}_{initial}$. For a circular motion, this change in momentum vector points towards the center of the circle.
$3$. According to Newton's second law, $\vec{F} = \frac{d\vec{p}}{dt}$. The force (tension in the string) is directed towards the center, which is the same direction as the change in momentum.
$4$. Since the momentum vector is tangential and the change in momentum vector is radial (towards the center), they are clearly not in the same direction.

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