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?

Respuesta :

Answer:

Angular velocity will be 2.843 rad/sec

Explanation:

We have given the radius r = 5.17 m

Centripetal acceleration [tex]a_c=1.5g=1.5\times 9.8=14.7m/sec^2[/tex]

We know that centripetal acceleration is given by

[tex]a_c=\frac{v^2}{r}[/tex]

And linear velocity is given by [tex]v=\omega r[/tex]

[tex]a_c=\frac{(\omega r)^2}{r}=\omega ^2r[/tex]

[tex]14.7=\omega ^2\times 5.17[/tex]

[tex]\omega =2.843rad/sec[/tex]