Chapter 8, Problem 4P

To determine

To Calculate: The angular acceleration of the blender blades as the blade slows down.

Answer to Problem 4P

  $-226.7{\text{rad/s}}^{\text{2}}$

Explanation of Solution

Given:

RPM of the Blades, $\text{RPM}=6500$ .

Time taken to come to rest, $t=3\text{s}$ .

Formula used:

  $\text{rad/s=RPM}\times \frac{\pi }{30}$ . $$

  $\alpha =\frac{\omega }{t}$

Where

  $\alpha$ is angular acceleration.

  $\omega$ is angular velocity.

  $\text{t}$ is time taken.

Calculation:

Substituting the given values

  $\omega$ =Velocity in rad/s = $6500\times \frac{\pi }{30}$ = $680.3\text{rad/s}$ .

Therefore, acceleration will be:

  $\alpha =-\frac{680.3}{3}=-226.7{\text{rad/s}}^{\text{2}}$ (negative because it is slowing down).

Conclusion:

Thus, the angular acceleration of the blades is $-226.7{\text{rad/s}}^{\text{2}}$ .