Respuesta :
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 [tex]1.7 m/s^2 \hat i+3.20m/s^2 \hat j[/tex] . At that instant and in unit-vector notation, what is the acceleration of the wallet?
Answer:
[tex]a'= 2.55 m/s^2\hat i + 4.8 m/s^2 \hat j[/tex]
Explanation:
Given: Purse is at radius, [tex]R=2.10 m[/tex]
Wallet is at radius, [tex]R'=3.15 m[/tex]
acceleration of the purse, [tex]a =[/tex] [tex]1.7 m/s^2 \hat i+3.20m/s^2 \hat j[/tex]
[tex]a=r\omega^2[/tex]
Both the purse and wallet would have same angular velocity [tex]\omega[/tex].
[tex]\sqrt \frac{a}{R}=\sqrt \frac{a'}{R'}[/tex]
[tex]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[/tex]
