Question

Max and maya are riding on a merry-go-round that rotates at a constant speed. if the merry-go-round makes 3.5 revolutions in 9.2 seconds, what is its angular speed?

Answer 1

Angular speed is given by 

w = number of revolutions/ total time

w = 3.5 revs / 9.2s = 0.38 revs/s

We can convert this result to radians per second, knowing that 1 rev = 2pi radians

w = 0.38 (2*pi) rads/s = 2.388 rads/ second

Answer 2

The angular speed of merry-go-round is $\fbox{\begin\\2.4\,{\text{rad/s}}\end{minispace}}$.

Further explanation:

Merry-go-round is an amusement ride which revolves around a center point situated at height from the ground. It acts like a circular wheel of some radius.

Given:

The number of revolutions is 3.5.

The time taken to complete the revolutions is 9.2 s.

Concept used:

The rate of change of angular separation with respect to time is known as the angular speed of the object.

The expression for the angular speed is given as.

$\fbox{\begin\\\omega= \dfrac{\theta }{t}\end{minispace}}$                             …… (1)

Here,$\omega$  is the angular speed, $\theta$  is the angular displacement and $t$ is the time period.

The time taken to complete one revolution is known as the time period.

The number of revolutions in one second is known as the frequency of circular motion.

The distance covered in one revolution is the one complete cycle that the ride took.

The distance covered in one complete is $2\pi \,{\text{rad}}$. So, the distance covered in 3.5 cycles is $7\pi \,{\text{rad}}$.

Substitute $7\pi \,{\text{rad}}$ for $\theta$  and $9.2 s$ for $t$ in equation (1).

$\begin{aligned}\omega &=\frac{{7\pi\,{\text{rad}}}}{{9.2\,{\text{s}}}}\\&=2.4\,{\text{rad/s}}\\\end{aligned}$

Thus, the angular speed of merry-go-round is $\fbox{\begin\\2.4\,{\text{rad/s}}\end{minispace}}$.

Learn more:

1.  Conservation of momentum https://brainly.com/question/9484203.

2.  Rotation of body https://brainly.com/question/3923773.

3. Angular speed of train https://brainly.com/question/9575487.

Answer Details:

Grade: College

Subject: Physics

Chapter: Angular motion

Keywords:

Revolution, time period, frequency, perimeter, radian, circle, circular motion, angular displacement, angular frequency, 9.2 sec, 3.5 rounds, 2.4rad/sec, 2.39rad/sec.