Final answer:
The linear velocity of a point on the rim of a wheel can be calculated using the formula v = rw. Given the diameter and angular velocity, the radius and rev/min are calculated and substituted into the formula to find the linear velocity. The linear velocity is approximately 532 feet per minute.
Step-by-step explanation:
The linear velocity of a point on the rim of a rotating wheel can be calculated using the formula v = rw, where v is the linear velocity, r is the radius of the wheel, and w is the angular velocity.
Given that the wheel has a diameter of 71 inches, we can calculate the radius by dividing the diameter by 2: r = 71 inches / 2 = 35.5 inches.
Next, we convert the angular velocity of 3 radians per second to rev/min using the conversion factor: w = 3 rad/s * (60 min/1 rev) = 180 rev/min.
Finally, we substitute the values into the formula: v = (35.5 inches) * (180 rev/min) = 6,390 inches/min.
To the nearest foot per minute, the linear velocity of a point on the rim is approximately 532 feet per minute.