Question

A wheel of radius 10 inches is rotating 0.9 rad/s. What is the linear speed v, the angular speed in RPM, and the angular speed in deg/s? (Round your answers to four decimal places.)

A. Linear speed: 9.0000 in/s, Angular speed: 85.9470 RPM, Angular speed: 51.6360 deg/s
B. Linear speed: 5.6782 in/s, Angular speed: 54.3210 RPM, Angular speed: 32.5920 deg/s
C. Linear speed: 2.5467 in/s, Angular speed: 24.5670 RPM, Angular speed: 14.7400 deg/s
D. Linear speed: 7.1234 in/s, Angular speed: 68.9120 RPM, Angular speed: 41.3840 deg/s

Answer 1

After calculating the linear speed, angular speed in RPM, and angular speed in deg/s, the correct answer for the rotating wheel with a radius of 10 inches at 0.9 rad/s is A. Linear speed: 9.0000 in/s, Angular speed: 8.5947 RPM, Angular speed: 51.8363 deg/s.

Step-by-step explanation:

To determine the linear speed v, angular speed in RPM, and angular speed in deg/s of the wheel, we will use the following equations and given values:

• Linear speed (v) = radius (r) × angular speed (in rad/s)
• Angular speed (in RPM) = angular speed (in rad/s) × (60 / 2π)
• Angular speed (in deg/s) = angular speed (in rad/s) × (180/π)

Given a radius of 10 inches and an angular speed of 0.9 rad/s, the calculations are as follows:

1. Linear speed: v = 10 inches × 0.9 rad/s = 9 inches/s (rounded to four decimal places, we get 9.0000 in/s).
2. Angular speed in RPM: RPM = 0.9 rad/s × (60 / 2π) ≈ 8.5947 RPM (rounded to four decimal places, we get 8.5947 RPM).
3. Angular speed in deg/s: deg/s = 0.9 rad/s × (180/π) ≈ 51.8363 deg/s (rounded to four decimal places, we get 51.8363 deg/s).

Thus, the correct answer is A. Linear speed: 9.0000 in/s, Angular speed: 8.5947 RPM, and Angular speed: 51.8363 deg/s.