Question

a merry go round has a radius of 8 meters makes 2 revolutions every 2.5 minutes. A. express the angular speed of the merry go around in radians per seconds. B. express the angular speed of the merry go round in rpms. C. what is the linear speed of a child seated 7 meters from the center.

Answer 1

a).
`v=83.77x10^(-3) rad/s`

b).
`v=0.8`rpm

c).v=0.5865 m/sec.

Step-by-step explanation:

Given:

`r=8m`

`v=(2rev)/(2.5minutes)`

a).

`2 rev*(2\pirad)/(1rev)=4\pi  rad`

`t=2.5minutes*(60s)/(1minute)=150s`

The angular speed in radians per seconds is

`v=(4\pi)/(150s)=83.77x10^(-3) rad/s`

b).

`v=(2rev)/(2.5minute)rpm`

`v=0.8`rpm

c)

Child's distance per revolution

(pi*2r) = 43.988 metres.

v=(43.988 x 0.0133333) = 0.5865 m/sec.