Question

A purse at radius 2.10 m and a wallet at radius 3.15 m travel in uniform circular motion on the floor of a merry-go-round as the ride turns. They are on the same radial line. At one instant, the acceleration of the purse is . At that instant and in unit-vector notation, what is the acceleration of the wallet?

Answer 1

Complete question is:

A purse at radius 2.10 m and a wallet at radius 3.15 m travel in uniform circular motion on the floor of a merry-go-round as the ride turns. They are on the same radial line. At one instant, the acceleration of the purse is $1.7 m/s^2 \hat i+3.20m/s^2 \hat j$ . At that instant and in unit-vector notation, what is the acceleration of the wallet?

Answer:

$a'= 2.55 m/s^2\hat i + 4.8 m/s^2 \hat j$    

Explanation:

Given: Purse is at radius, $R=2.10 m$

Wallet is at radius, $R'=3.15 m$

acceleration of the purse, $a =$ $1.7 m/s^2 \hat i+3.20m/s^2 \hat j$

$a=r\omega^2$

Both the purse and wallet would have same angular velocity $\omega$.

$\sqrt \frac{a}{R}=\sqrt \frac{a'}{R'}$

$a'=\frac{a}{R}\times R \\ \Rightarrow a' = \frac{1.7 m/s^2 \hat i+3.20m/s^2 \hat j}{2.10 m}\times 3.15 m \\ a'= 2.55 m/s^2\hat i + 4.8 m/s^2 \hat j$