A Ferris wheel,rotating initially at an angular speed of 0.50 rad/s,accelerates over a 8.0-s interval at a rate of 0.05 rad/s².What angular displacement does the Ferris wheel undergo in this 7.00-s interval? A) 1.60 rad B) 4.20 rad C) 5.60 rad D) 7.20 rad E) 4.40 rad

Question

Quizplus · Accepted Answer

Using the formula for angular displacement:

θ = ωi*t + (1/2)*α*t^2

Where:
ωi = initial angular velocity = 0.50 rad/s
t = time interval = 8.0 s
α = angular acceleration = 0.05 rad/s^2

Plugging in the given values:

θ = (0.50 rad/s)*(8.0 s) + (1/2)*(0.05 rad/s^2)*(8.0 s)^2
θ = 4.00 rad + 1.60 rad
θ = 5.60 rad

Therefore, the angular displacement the Ferris wheel undergoes in this 8.0-s interval is 5.60 rad.

A Ferris Wheel,rotating Initially at an Angular Speed of 0