A purse at radius 2.00 m and a wallet at radius 3.00 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 (2.00 m/s2 ) (4.00 m/s2 ) .At that instant and in unit-vector notation, what is the acceleration of the wallet

They are on the same radial line. At one instant, the acceleration of the purse is (2.00 m/s2 ) i + (4.00 m/s2 ) j .At that instant and in unit-vector notation, what is the acceleration of the wallet

Answer:

aw = 3 i + 6 j m/s2

Explanation:

Since both objects travel in uniform circular motion, the only acceleration that they suffer is the centripetal one, that keeps them rotating.
It can be showed that the centripetal acceleration is directly proportional to the square of the angular velocity, as follows:

[tex]a_{c} = \omega^{2} * r (1)[/tex]

Since both objects are located on the same radial line, and they travel in uniform circular motion, by definition of angular velocity, both have the same angular velocity ω.

∴ ωp = ωw (2)

⇒ [tex]a_{p} = \omega_{p} ^{2} * r_{p} (3)[/tex]

[tex]a_{w} = \omega_{w}^{2} * r_{w} (4)[/tex]

Dividing (4) by (3), from (2), we have:

[tex]\frac{a_{w} }{a_{p}} = \frac{r_{w} }{r_{p}}[/tex]

Solving for aw, we get:

[tex]a_{w} = a_{p} *\frac{r_{w} }{r_{p} } = (2.0 i + 4.0 j) m/s2 * 1.5 = 3 i +6j m/s2[/tex]