Final answer:
To find the linear velocity of a point on the edge of a rotating wheel, we convert the rotational speed to radians per second, calculate the radius in feet, and then use the formula for linear velocity. The correct linear velocity is A. 339 ft/min.
Step-by-step explanation:
To find the linear velocity of a point on the edge of a wheel rotating at 48 times per minute with a diameter of 27 inches, we need to use the formula ℓ = ωr, where ℓ is the linear velocity, ω is the angular velocity, and r is the radius of the wheel.
First, we convert the rotational speed into revolutions per second (rev/s) by dividing 48 rev/min by 60 s/min, which gives us 0.8 rev/s.
Next, we convert the revolutions per second to radians per second by multiplying by 2π (since there are 2π radians in one revolution): ω = 0.8 rev/s × 2π rad/rev = 5.024 rad/s.
The radius of the wheel is half the diameter, so r = 27 inches / 2 = 13.5 inches. Converting inches to feet, we have r = 13.5 inches × 1 foot/12 inches = 1.125 feet.
Now we can calculate the linear velocity: ℓ = ωr = 5.024 rad/s × 1.125 feet = 5.652 feet/s. To find feet per minute, we multiply by 60 s/min: ℓ = 5.652 feet/s × 60 s/min = 339 ft/min.
The correct answer is A. 339 ft/min