Question

A purse at radius 2.30 m and a wallet at radius 3.45 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

The acceleration of the wallet is
`3\hat{i}+6\hat{j}`

Step-by-step explanation:

Given that,

Radius of purse r= 2.30 m

Radius of wallet r'= 3.45 m

Acceleration of the purse
`a=2\hat{i}+4.00\hat{j}`

We need to calculate the acceleration of the wallet

Using formula of acceleration

`a=r\omega^2`

Both the purse and wallet have same angular velocity

`\omega=\omega'`

`\sqrt{(a)/(r)}=\sqrt{(a')/(r')}`

`(a)/(r)=(a')/(r')`

`(a')/(a)=(r')/(r)`

`(a')/(a)=(3.45)/(2.30)`

`(a')/(a)=(3)/(2)`

`a'=(3)/(2)*(2\hat{i}+4.00\hat{j})`

`a'=3\hat{i}+6\hat{j}`

Hence, The acceleration of the wallet is
`3\hat{i}+6\hat{j}`