KCET · Physics · Laws of Motion
A rotating wheel changes angular speed from \( 1800 \mathrm{rpm} \) to \( 3000 \mathrm{rpm} \) in \( 20 \mathrm{~s} \). What is the
angular acceleration assuming to be uniform ?
- A \( 60 \) п rad s \( ^{-2} \)
- B 90п rad s \( ^{-2} \)
- C \( 2 \Pi \mathrm{rad} s^{-2} \)
- D 40п rad s \( ^{-2} \)
Answer & Solution
Correct Answer
(C) \( 2 \Pi \mathrm{rad} s^{-2} \)
Step-by-step Solution
Detailed explanation
For angular speed of \( 1800 \mathrm{rpm} \)
\( \omega_{1}=2 \Pi f_{1}=2 \Pi\left(\frac{1800}{60}\right)=60 \Pi \mathrm{rad} s^{-1} \)
For angular speed of \( 3000 \mathrm{rpm} \)
\( \omega_{2}=2 \Pi f_{2}=2 \Pi\left(\frac{3000}{60}\right)=100 \Pi \mathrm{rad} s^{-1} \)
Therefore, angular acceleration \( =\frac{\omega_{2}-\omega_{1}}{t}=\frac{100 \Pi-60 \Pi}{20} \)
\( =\frac{40 \Pi}{20}=2 \Pi \)
Thus, angular acceleration of rotating wheel \( =2 \pi \mathrm{rads}^{-2} \)
\( \omega_{1}=2 \Pi f_{1}=2 \Pi\left(\frac{1800}{60}\right)=60 \Pi \mathrm{rad} s^{-1} \)
For angular speed of \( 3000 \mathrm{rpm} \)
\( \omega_{2}=2 \Pi f_{2}=2 \Pi\left(\frac{3000}{60}\right)=100 \Pi \mathrm{rad} s^{-1} \)
Therefore, angular acceleration \( =\frac{\omega_{2}-\omega_{1}}{t}=\frac{100 \Pi-60 \Pi}{20} \)
\( =\frac{40 \Pi}{20}=2 \Pi \)
Thus, angular acceleration of rotating wheel \( =2 \pi \mathrm{rads}^{-2} \)
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