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

Answer:

Angular velocity will be 2.843 rad/sec

Explanation:

We have given the radius r = 5.17 m

Centripetal acceleration $a_c=1.5g=1.5\times 9.8=14.7m/sec^2$

We know that centripetal acceleration is given by

$a_c=\frac{v^2}{r}$

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

$a_c=\frac{(\omega r)^2}{r}=\omega ^2r$

$14.7=\omega ^2\times 5.17$

$\omega =2.843rad/sec$