A body rotating with an angular speed of 600 rpm is uniformly accelerated to 1800 rpm in 10 s. The number of rotations made in the process is …… .

rpm stands for rotations per minute.

rps stands for rotations per second.

Given, initial angular speed, ${\mathrm{\omega }}_0=600\mathrm{rpm}=10\mathrm{rps}$

Final angular speed, ${\mathrm{\omega }}_{\mathrm{F}}=1800\mathrm{rpm}=30\mathrm{rps}$

Time, t = 10 s

$\because$ We know that

$\begin{array}{l}{\mathrm{\omega }}_{\mathrm{F}}={\mathrm{\omega }}_0+\mathrm{\alpha t}\\ 30=10+\mathrm{\alpha }\times 10\Rightarrow \frac{30-10}{10}=\mathrm{\alpha }\\ \Rightarrow \mathrm{\alpha }=\frac{20}{10}=2{\mathrm{rps}}^2\end{array}$

Angular displacement is calculated by the rotational equation of motion as

$\mathrm{\theta }={\mathrm{\omega }}_0\mathrm{t}+\frac{1}{2}{\mathrm{\alpha t}}^2$

where, $\mathrm{\theta }$ is the angular displacement.

$\begin{array}{l}\Rightarrow \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\mathrm{\theta }=10\times 10+\frac{1}{2}\times 2\times (10{)}^2\\ \Rightarrow \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\mathrm{\theta }=100+100\Rightarrow \mathrm{\theta }=200 \mathrm{rotations}\end{array}$