An auto race is held on a circular track. A car completes one lap in a time of 16.9 s, with an average tangential speed of 48.1 m/s. Find the following
(a) the average angular speed
(b) the radius of the track
i found part a which was .3716 but need help with part b please
one lap in 16.9s? That is 2PI radians/16.9s which is the angular speed.
b. angularspeed*radius= tangential speed, find radius.
To find the radius of the track, we can use the average tangential speed and the average angular speed. Recall that the relationship between linear speed (v) and angular speed (ω) is given by the formula:
v = ω * r
where v is the linear speed, ω is the angular speed, and r is the radius of the circular track. We can rearrange this equation to solve for the radius:
r = v / ω
Given that the average tangential speed (v) is 48.1 m/s and the average angular speed (ω) is 0.3716 rad/s, we can substitute these values into the equation:
r = 48.1 m/s / 0.3716 rad/s
Using a calculator, we can calculate the radius:
r ≈ 129.59 m
Therefore, the radius of the circular track is approximately 129.59 meters.