Since Gottfried works a desk job as a lawyer, he likes to exercise on his lunch break. His wings get a workout when he flies to and from work, so he needs to exercise his legs. To do this, he runs around a circular track. If he can run 4 laps in 2 minutes, what is his angular velocity in radians per second (rad/s)? (Hint: start by figuring out how many radians are in 4 laps, and then figuring out how many seconds are in 2 minutes.)
d = 4Laps * 6.28rad/Lap = 25.12 rad.
Va = 25.12rad/120s =
To find Gottfried's angular velocity in radians per second (rad/s), we need to determine how many radians he covers in a given time.
First, let's calculate how many radians are in 4 laps around the circular track. Each lap around the track covers 360 degrees since it's a full circle. Since there are 2π radians in one full circle, we can calculate the number of radians in 4 laps as follows:
4 laps * 360 degrees per lap * (π/180) radians per degree = 8π radians
Next, we need to determine how many seconds are in 2 minutes. Since there are 60 seconds in a minute, we multiply 2 minutes by 60 seconds per minute to find:
2 minutes * 60 seconds per minute = 120 seconds
Now we can calculate Gottfried's angular velocity by dividing the number of radians (8π radians) by the time (120 seconds):
Angular velocity = 8π radians / 120 seconds
Simplifying this gives us:
Angular velocity = (2π/30) rad/s
Therefore, Gottfried's angular velocity is (2π/30) rad/s.