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?

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ABIDEMIOKINGO ABIDEMIOKINGO · Answer 1

Answer:

155.80rad/s

Explanation:

Using the equation of motion to find the angular acceleration:

[tex]\omega_f = \omega_i + \alpha t[/tex]

[tex]\omega_f[/tex] is the final angular velocity in rad/s

[tex]\omega_i[/tex] is the initial angular velocity in rad/s

[tex]\alpha[/tex] is the angular acceleration

t is the time taken

Given the following

[tex]\omega_f = 6100rpm[/tex]

Time = 4.1secs

Convert the angular velocity to rad/s

1rpm = 0.10472rad/s

6100rpm = x

x = 6100 * 0.10472

x = 638.792rad/s

[tex]\omega_f = 638.792rad/s\\[/tex]

Get the angular acceleration:

Recall that:

[tex]\omega_f = \omega_i + \alpha t[/tex]

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