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What are the differences between a nonuniform circular motion and a uniform circular motion? (Two points of distinction) Give examples.

Vidyadip · Accepted Answer

(i) Nonuniform circular motion :
1. The angular and tangential accelerations are non-zero, so that linear and angular speeds both change with time.
$
\vec{\alpha}=\frac{d \vec{\omega}}{d t} \text { and } \overrightarrow{a_t}=\frac{d \vec{v}}{d t}=\vec{\alpha} \times \vec{r}
$
If a particle in nonuniform circular motion is speeding up, $\vec{\alpha}$ is in the direction of $\vec{\omega}$ and $\overrightarrow{a_t}$ is in the direction of $\vec{v}$; if the particle is slowing down, $\vec{\alpha}$ is opposite to $\vec{\omega}$ and $\overrightarrow{a_t}$ is opposite to $\vec{v}$.
2. The net linear acceleration, being the resultant of the radial and tangential accelerations, is not radial, $\vec{a}=\overrightarrow{a_{\mathrm{c}}}+\overrightarrow{a_t}$,
3. The magnitudes of the centripetal acceleration and the centripetal force are not constant.
4. Example: Motion of the tip of a fan blade when the fan is speeding up or slowing down.
(ii) Uniform circular motion :
1. The angular and tangential accelerations are zero, so that linear speed and angular velocity are constant.
2. The net linear acceleration is radially inward, i.e., centripetal.
3. The magnitudes of the centripetal acceleration and the centripetal force are also constant.
4. Example: Motion of the tips of the hands of a mechanical clock.

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