A 45-kg woman is riding a Ferris wheel of radius 15 m at a constant speed.The angular speed of the Ferris wheel that would make her weightless at the top is
A)0.81 rad/s
B)0.50 rad/s
C)0.10 rad/s
D)0.65 rad/s
E)0.213 rad/s

Question

Quizplus · Accepted Answer

For a person to feel weightless at the top of the Ferris wheel, the centripetal force must equal the gravitational force acting on them. The centripetal force ($F_c$) is given by $F_c = m\omega^2r$, where $m$ is the mass, $\omega$ is the angular speed, and $r$ is the radius. The gravitational force ($F_g$) is given by $F_g = mg$, where $g$ is the acceleration due to gravity (approximately $9.8 m/s^2$). Setting $F_c = F_g$, we get $m\omega^2r = mg$. Simplifying, $\omega^2 = g/r$. Substituting $g = 9.8 m/s^2$ and $r = 15 m$, we find $\omega = \sqrt{9.8/15}$, which calculates to approximately $0.81 rad/s$.

A 45-Kg Woman Is Riding a Ferris Wheel of Radius