Question

f the merry-go-round, whereas Zak is two meters from the center. Abbie’s acceleration is ___________ Zak’s acceleration. Two children are riding on a merry-go-round that is rotating with a constant angular speed. Abbie is one meter from the center of the merry-go-round, whereas Zak is two meters from the center. Abbie’s acceleration is ___________ Zak’s acceleration. a quarter of twice equal to half of four times

Answer 1

Answer:

The acceleration of Abbie is half of the Zak's.

Explanation:

The centripetal acceleration of an object on a circular path is given by :

$a=r\omega^2$

Two children are riding on a merry-go-round that is rotating with a constant angular speed. Let $r_1$ is distance of Abbie from the merry-go-round and $r_2$ is distance of Zak's from the merry-go-round. Acceleration of Abbie is :

$a_1=r_1\omega^2$ ...... (1)

$r_1=1\ m$

Acceleration of Zak's is :

$a_2=r_2\omega^2$ .......(2)

$r_2=2\ m$

Dividing equation (1) and (2) we get :

$\dfrac{a_1}{a_2}=\dfrac{r_1}{r_2}\\\\\dfrac{a_1}{a_2}=\dfrac{1}{2}\\\\a_1=\dfrac{a_2}{2}$

So, the acceleration of Abbie is half of the Zak's.