Angular Deceleration of Flywheel due to Rotation Motion

[thereddevils]

Homework Statement

A flywheel of radius 0.20 m with moment of inertia 0.15 kg/m^2 rotates at 180 revolution per minute . A tangential force is applied on the rim of the flywheel and it stops after 12 revolutions.Calculate the angular deceleration .

Homework Equations

The Attempt at a Solution

The initial angular velocity is 18.9 rad/s after conversion. The time taken for 12 revolutions is 4s (since it can rotate 180 times in 60 s , so in 4 s , it can rotate 12 times) . Final angular velocity is 0 .

Using $$\omega_f=\omega_i+\alpha t$$

$$0=18.9+4\alpha$$

solving this , i got 4.37 sec

but the ans given 2.37 sec, where did i go wrong ?

 

[Doc Al]

The time taken for 12 revolutions is 4s (since it can rotate 180 times in 60 s , so in 4 s , it can rotate 12 times) .

That would be true if the angular velocity were constant, but it's not. The wheel is slowing down. Hint: What's the average speed during its acceleration?

 

[thereddevils]

That would be true if the angular velocity were constant, but it's not. The wheel is slowing down. Hint: What's the average speed during its acceleration?

thanks Doctor , so if i take the average velocity , then the time,t =4s would be valid in my calculations ?

a=v/t=(18.9/2)/4=2.37

 

[Doc Al]

thanks Doctor , so if i take the average velocity , then the time,t =4s would be valid in my calculations ?

The thing to do is use the average angular speed to find the correct time. (4s is not correct.) Then you can use your original equation to find the acceleration.

 

[thereddevils]

The thing to do is use the average angular speed to find the correct time. (4s is not correct.) Then you can use your original equation to find the acceleration.

sorry doc , i still don get it .

Is the average simply 18.9/2=9.45 s

Then , i am not sure how to use this to find time .

 

[Doc Al]

sorry doc , i still don get it .

Is the average simply 18.9/2=9.45 s

Yes. (The units are radians/sec.)

Then , i am not sure how to use this to find time .

Use the rotational analog to Distance = Ave Speed X Time
(The "distance" will be the angle in radians.)

 

[thereddevils]

Yes. (The units are radians/sec.)


Use the rotational analog to Distance = Ave Speed X Time
(The "distance" will be the angle in radians.)

thanks i was too hung up with the 180 revolutions as compared to 12 revolutions so a final check ,

the angular displacement is 2pi x 12=75.4 (Initially , i though of 2pi x 0.2 x12 , this would be linear displacement right ?)

75.4=9.45t , t is approximately 8s .

0=18.9+8a

a=-2.37 rad/s^2

 

[Doc Al]

All good!