Question

a wheel of radius 6 inches is rotating at 1.75 rad/s. round answers to 2 decimal places, where necessary.
what is the linear speed v?

inch/s
what is the angular speed in rpm?

rpm
what is the angular speed in degrees/s?

°/s
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Explanation:

Step1: Calculate linear speed

The formula for linear speed \(v = r\omega\), where \(r = 6\) inches and \(\omega=1.75\) rad/s.
\(v=6\times1.75 = 10.50\) inch/s

Step2: Convert angular speed from rad/s to RPM

We know that \(1\) revolution \( = 2\pi\) radians and \(1\) minute \(=60\) seconds.
The formula for converting from \(\omega\) (in rad/s) to RPM is \(n=\frac{\omega}{2\pi}\times60\)
Substitute \(\omega = 1.75\) rad/s: \(n=\frac{1.75}{2\pi}\times60=\frac{105}{2\pi}\approx16.71\) RPM

Step3: Convert angular speed from rad/s to degrees/s

We know that \(\pi\) radians \( = 180^{\circ}\)
The formula for converting from \(\omega\) (in rad/s) to degrees/s is \(\theta=\omega\times\frac{180^{\circ}}{\pi}\)
Substitute \(\omega = 1.75\) rad/s: \(\theta = 1.75\times\frac{180^{\circ}}{\pi}\approx100.27^{\circ}/s\)

Answer:

10.50 inch/s
16.71 RPM
100.27°/s