Question

A Ferris Wheel, starting from rest, undergoes a constant angular acceleration of 0.033 rad/s2 to get to its final operating angular velocity of 0.24 rad/s. (a) How long does it take the Ferris Wheel to get to its operating angular velocity? (b) How many revolutions does it make during this time interval?

Answer 1

Initial angular velocity ₀ = 0 rad/s. Final angular velocity = 0.24 rad/s.

Angular acceleration = 0.033 rad/s^{​​​​​​2}​​​​​.

a) kinematical equation of rotational motion: = ₀ + t

The time to gets it operational angular velocity

t =( – ₀ )/ = ( 0.24–0)/0.033 = 7.27 s

b) Another kinematical equation of rotational motion : = ₀t + 0.5 * *t^{​​​​​​2}

Angular displacement in that time = 0 + 0.5 × 0.033 × (7.27)² = 0.87 radian.

2 π radian displacement = 1 revolution

0.87 radian displacement = 0.87/ 2π = 0.14 revolution