Question

1. a wheel with a radius of 2ft has a max rpm of 500. what is the maximu linear velocity ft/s? select the closest answer. 105ft/s 2) a wheel with a diameter of 2.5ft has a max rpm of 800. what is the maximum linear velocity in ft/s? select the closest answer.

Explanation:

Step1: Recall linear velocity formula

Linear velocity \(v = r \times \omega\), where \(\omega\) is angular velocity in rad/s.

Step2: Convert RPM to rad/s (Q1)

Angular velocity \(\omega = 500 \times \frac{2\pi}{60} = \frac{50\pi}{3}\) rad/s

Step3: Calculate Q1 linear velocity

Radius \(r=2\) ft, so \(v = 2 \times \frac{50\pi}{3} = \frac{100\pi}{3} \approx 104.72\) ft/s

Step4: Find radius for Q2

Diameter=2.5 ft, so \(r = \frac{2.5}{2} = 1.25\) ft

Step5: Convert RPM to rad/s (Q2)

Angular velocity \(\omega = 800 \times \frac{2\pi}{60} = \frac{80\pi}{3}\) rad/s

Step6: Calculate Q2 linear velocity

\(v = 1.25 \times \frac{80\pi}{3} = \frac{100\pi}{3} \approx 104.72\) ft/s

Answer:

1. 105ft/s
2. 105ft/s