Question:
A train is moving on a circular curve of radius 1500 m at the rate of 66 km per hour. Through what angle has it turned in 10 seconds?
Solution:
Radius = 1500 m
Train speed at rate of $66 \mathrm{~km} / \mathrm{hr}=18.33 \mathrm{~m} / \mathrm{s}$
Therefore, Distance covered in 1 second $=18.33 \mathrm{~m}$
Distance covered in 10 second $=18.33 \times 10=183.33 \mathrm{~m}$
We know that $\theta=$ Distance $/$ radius
$\theta=183.33 / 1500$
$=0.122$ radian
Therefore $\theta=0.122 \times \frac{180}{\pi}=7^{\circ}$