Question

A Ferris wheel initially rotating 0.1 rad clockwise breaks, and the angular acceleration is 0.015 rad. Before the break is applied, how many seconds have passed?

a) 6.67 seconds
b) 15 seconds
c) 0.0067 seconds
d) 67 seconds

Answer 1

To calculate the time elapsed before the brakes were applied, we use the formula t = ω₀ / α, with the given initial angular velocity of 0.1 rad/s and angular acceleration of 0.015 rad/s². The calculated time is 6.67 seconds.

Step-by-step explanation:

The question is asking us to determine how many seconds have passed since the initial state of a Ferris wheel rotating clockwise until the brakes were applied. Given the initial angular velocity (ω₀) as 0.1 rad/s clockwise and an angular acceleration (α) of 0.015 rad/s², we use the formula for angular acceleration α = (ω - ω₀) / t, where ω is the final angular velocity and t is the time in seconds.

Since the brakes are applied, which means the wheel is decelerating, the angular acceleration would be negative in value when considering the direction: α = -0.015 rad/s². However, we seek the duration of rotation before applying the brakes (i.e., when ω is still ω₀). Therefore, we use the formula in its basic form without a sign for the angular acceleration: t = ω₀ / α.

After substituting the values into the formula t = 0.1 / 0.015, we calculate the time as 6.67 seconds.