Final answer:
The minimum tread depth for the steer-tire is 3000 rev/min, and the centripetal acceleration at the edge of the tire is 750 m/s^2.
Step-by-step explanation:
To find the angular speed of the tire, we can rearrange the equation v = r, where v is the speed of the tire, r is the radius of the tire, and is the angular speed. Given that v = 15.0 m/s and r = 0.300 m, we can solve for . Plugging in the values, we get = 15.0 m/s / 0.300 m = 50 rev/s.
However, the question asks for the speed in rev/min. To convert from rev/s to rev/min, we multiply by 60 (since there are 60 seconds in a minute). So, the tires are rotating at 50 rev/s * 60 = 3000 rev/min.
The centripetal acceleration at the edge of the tire can be calculated using the formula a = rω^2, where a is the centripetal acceleration, r is the radius of the tire, and ω is the angular speed. Substituting the values, we get a = (0.300 m) * (50 rev/s)^2 = 750 m/s^2.