Question

A particle is revolving on a circular path with a constant speed. If its speed and radius of the path are doubled, then its angular speed will

• A. Remain unchanged
• B. Gets doubled
• C. Gets quadrupled
• D. Gets halved

Answer 1

The correct option is A Remain unchanged

Let the initial speed of the particle be v and the initial radius of the path be r.
∴ Angular speed, $\omega =\frac{v}{r}$
According to the question:
New speed, v' = 2v
New radius, r' = 2r
New angular speed, ${\omega }^{\prime }=\frac{v^{\prime }}{r^{\prime }}=\frac{2v}{2r}$
$\Rightarrow {\omega }^{\prime }=\frac{v}{r}$
$\Rightarrow {\omega }^{\prime }=\omega$
Thus, the angular speed remains unchanged.
Hence, the correct answer is option (a).