Question

The blades in a blender rotate at a rate of 6100 rpm. When the motor is turned off during operation, the blades slow to rest in 4.1s. What is the angular acceleration as the blades slow down?

Answer 1

Answer:

155.80rad/s

Explanation:

Using the equation of motion to find the angular acceleration:

$\omega_f = \omega_i + \alpha t$

$\omega_f$ is the final angular velocity in rad/s

$\omega_i$  is the initial angular velocity in rad/s

$\alpha$ is the angular acceleration

t is the time taken

Given the following

$\omega_f = 6100rpm$

Time = 4.1secs

Convert the angular velocity to rad/s

1rpm = 0.10472rad/s

6100rpm = x

x = 6100 * 0.10472

x  = 638.792rad/s

$\omega_f = 638.792rad/s$

Get the angular acceleration:

Recall that:

$\omega_f = \omega_i + \alpha t$

638.792 = 0 + ∝(4.1)

4.1∝ = 638.792

∝ = 638.792/4.1

∝ = 155.80rad/s

Hence the angular acceleration as the blades slow down is 155.80rad/s