Question

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?

A. 76.2 , {rad/s}, 727.3 , {rev/min}
B. 83.8 , {rad/s}, 800.2 , {rev/min}
C. 90.5 , {rad/s}, 872.7 , {rev/min}
D. 98.0 , {rad/s}, 943.5 , {rev/min}

Answer 1

The angular velocity of the truck's tires is approximately 76.2 rad/s, and when converted to revolutions per minute, it is approximately 727.3 rev/min. Therefore, the correct answer is A.

Step-by-step explanation:

To find the angular velocity of the rotating tires in radians per second (rad/s), we use the relationship between linear velocity (v), the radius of the tire (r), and the angular velocity (ω), which is v = ωr. In this case, the linear velocity (v) is 32.0 m/s and the radius (r) is 0.420 m. This gives:

ω = v / r = 32.0 m/s / 0.420 m = 76.19 rad/s (approximately).

To convert the angular velocity to revolutions per minute (rev/min), you must first convert radians per second to revolutions per second by dividing by 2π (since there are 2π radians in a revolution). You then multiply by 60 to convert from seconds to minutes:

rev/s = ω / (2π) = 76.19 rad/s / (2π) = 12.12 rev/s (approximately).

rev/min = rev/s × 60 = 12.12 rev/s × 60 = 727.2 rev/min (approximately).

Therefore, the correct answer is A. 76.2 rad/s, 727.3 rev/min.