1) Compute the angular velocity in rad/s of the crankshaft of an automobile engine that is rotating at 4200rev/min.439.6rad/s

Here's how to convert revolutions per minute (rpm) to radians per second (rad/s):<br /><br />1. **Convert revolutions to radians:** There are $2\pi$ radians in one revolution.<br /><br />2. **Convert minutes to seconds:** There are 60 seconds in one minute.<br /><br />So, the conversion factor is $(2\pi \text{ rad/rev}) \times (\frac{1 \text{ min}}{60 \text{ s}})$.<br /><br />Applying this to the given rotation speed:<br /><br />Angular velocity = $4200 \frac{\text{rev}}{\text{min}} \times \frac{2\pi \text{ rad}}{\text{rev}} \times \frac{1 \text{ min}}{60 \text{ s}} = 4200 \times \frac{2\pi}{60} \frac{\text{rad}}{\text{s}} = 140\pi \frac{\text{rad}}{\text{s}} \approx 439.82 \text{ rad/s}$<br /><br />Therefore, the angular velocity is approximately $439.82$ rad/s.<br />