What is the Angular Position?

A Ferris wheel rotates at an angular velocity of 3.9×10^-2 rad/s . At t=0, your friend Seth is at the very top of the ride.

What is Seth’s angular position at t= 3.4 min measured counterclockwise from the top?

Give your answer as an angle in degrees between 0° and 360°.

Known Variables:

Angular Velocity (ω): 3.9×10^-2 rad/s

Time _initial: t_initial=0
Time _final: t_final=3.4
First step is to convert minutes into seconds.

t= 3.4

3.4 × 60 = 204 seconds
Radians Traveled:

204 × 3.9×10^-2 rad/s =7.95 radians
Convert to degrees.

7.95 × 180 / π=  455.84°

This is the measurement of how far Seth has traveled starting from the origin at the top. To find out how far he has gone through the range of 360°, subract from 360°

455.84°-360°=95.84°

θ=96°