Question

a) A boy is riding on a merry-go-round that rotates at a constant speed. If the merry-go-round makes 3.0 revolutions in 6.0 seconds. What is its angular speed in revolutions/second and in radians/second?

Answer 1

Angular speed = 0.5 revolutions/second = 3.14 rad/s

Step-by-step explanation:

a) The merry-go-round makes 3.0 revolutions in 6.0 seconds

Time taken for 3 revolutions = 6 s

Time taken for 1 revolution = 6÷3 = 2 s

That is period, T = 2 s

We know that

`\texttt{Angular speed},\omega =(2\pi )/(T)`

Substituting

`\texttt{Angular speed},\omega =(2\pi )/(2)=3.14rad/s\\\\\texttt{Angular speed},\omega =(2\pi )/(2* 2\pi)=0.5revolutions/s`

Angular speed = 0.5 revolutions/second = 3.14 rad/s