Q130 / 160 · AP EAMCET 2005 · Physics
Identify the increasing order of the angular velocities of the following
1. earth rotating about its own axis
2. hour's hand of a clock
3. second's hand of a clock
4. flywheel of radius $2 \mathrm{~m}$ making $300\mathrm{rpm}$
- Correct answerA1,2,3,4
- B3,4,1,2
- C3,4,1,2
- D4,1,2,3
Solution
(1) Angular velocity of earth,
$\begin{aligned}
\omega_1 & =\frac{2 \pi}{T}=\frac{2 \pi}{24 \times 60 \times 60} \\
& =\frac{2 \pi}{86400} \mathrm{rad} / \mathrm{s}
\end{aligned}$
(2) Angular velocity of hour's hand of a clock,
$\begin{aligned}
\omega_2 & =\frac{2 \pi}{T} \\
& =\frac{2 \pi}{12 \times 60 \times 60}=\frac{2 \pi}{43200} \mathrm{rad} / \mathrm{s}
\end{aligned}$
(3) Angular velocity of second's hand of a clock,
$\omega_3=\frac{2 \pi}{T}=\frac{2 \pi}{1 \times 60}=\frac{2 \pi}{60} \mathrm{rad} / \mathrm{s}$
(4) Angular velocity of flywheel,
$\begin{aligned}
\omega_4 & =2 \pi n=2 \pi \times \frac{300}{60} \\
& =2 \pi \times 5 \mathrm{rad} / \mathrm{s}=10 \pi \mathrm{rad} / \mathrm{s}
\end{aligned}$
So, the increasing order is
$1 < 2 < 3 < 4$
Hence, the correct answer is option: 'A'.