A race car makes two and a half laps around a circular track in 4.5 min. What is the car's average angular speed?
To find the car's average angular speed, we need to calculate the number of radians the car has traveled per unit of time. The formula for angular speed is given by:
Angular Speed = θ / t
Where:
- θ is the angle traveled
- t is the time taken
In this case, the car makes two and a half laps around the track. Since one lap is equivalent to a full circle, the car has traveled 2.5 x 2π radians around the track.
Now, to find the average angular speed, we divide the total angle traveled by the time taken to cover that distance.
Total angle traveled = 2.5 x 2π radians
Time taken = 4.5 min
First, we need to convert the time taken to seconds since the SI unit for time in the formula is seconds.
1 min = 60 seconds
Therefore, 4.5 min = 4.5 x 60 seconds = 270 seconds.
Now we can substitute the values into the formula:
Angular Speed = (2.5 x 2π) / 270
Simplifying:
Angular Speed = 5π / 270
Thus, the car's average angular speed is 5π/270 radians per second.
That would seem to depend upon how big the track is.
Divide 2.5 times the track circumference by the time.