Question

A fairground ride spins its occupants inside a flying saucer-shaped container. If the horizontal circular path the riders follow has a radius of 5.17 m, at what angular velocity will the riders be subjected to a centripetal acceleration whose magnitude is equal to 1.50 times the acceleration due to gravity?

Answer 1

Angular velocity will be 2.843 rad/sec

Step-by-step explanation:

We have given the radius r = 5.17 m

Centripetal acceleration
`a_c=1.5g=1.5* 9.8=14.7m/sec^2`

We know that centripetal acceleration is given by

`a_c=(v^2)/(r)`

And linear velocity is given by
`v=\omega r`

`a_c=((\omega r)^2)/(r)=\omega ^2r`

`14.7=\omega ^2* 5.17`

`\omega =2.843rad/sec`