A truck with 0.420-m-radius tires travels at 32.0 m/s. What is the angular velocity of the rotating tires in radians per second? What is this in rev/min?

To solve this problem, we need to use the relationship between linear velocity (v), angular velocity (ω), and the radius (r) of the circle. This relationship is given by the equation:

v = ω * r

We can rearrange this equation to solve for ω:

ω = v / r

Given that v = 32.0 m/s and r = 0.420 m, we can substitute these values into the equation:

ω = 32.0 m/s / 0.420 m = 76.19 rad/s

This is the angular velocity in radians per second.

To convert this to revolutions per minute, we need to use the fact that one revolution is equal to 2π radians and one minute is equal to 60 seconds. Therefore, we can convert 76.19 rad/s to rev/min by multiplying by (1 rev / 2π rad) * (60 s / 1 min):

ω = 76.19 rad/s * (1 rev / 2π rad) * (60 s / 1 min) = 727.3 rev/min

So, the angular velocity of the tires is 76.19 rad/s or 727.3 rev/min.