Angular Acceleration Problem Why am I not right?

[tjohn101]

Homework Statement

The blades in a blender rotate at a rate of 7900 rpm. When the motor is turned off during operation, the blades slow to rest in 4.0 s. What is the angular acceleration as the blades slow down?

Vi= 7900 rpm = 82.72860654 rad/sec (This may be my error)
Vf= 0
t= 4 secs

Homework Equations

$$v = v_0 + a t$$

The Attempt at a Solution

I've tried solving for a in the answer above but the answer is incorrect.. I did:

0 = 82.72860654 + a(4)
and when solved got an answer of -20.68215164. I'm unsure of why this is NOT correct. Any help is greatly appreciated.

I think the problem may be in my conversions to rad/sec or maybe I am forgetting to convert something.

 

[Doc Al]

Vi= 7900 rpm = 82.72860654 rad/sec (This may be my error)

You're off by a factor of ten.

 

[tjohn101]

You're off by a factor of ten.

Please tell me if this is the right method:

(7900*2pi)/60

If I do this then I get 827.2860654. Does that sound correct?

 

[Doc Al]

Please tell me if this is the right method:

(7900*2pi)/60

If I do this then I get 827.2860654. Does that sound correct?

Perfect!

 

[tjohn101]

Perfect!

Okay, and when I solve using the equation above I get the acceleration as being -206.8215164. It is already in rad/sec^2, correct? No conversions needed there?

 

[Doc Al]

Okay, and when I solve using the equation above I get the acceleration as being -206.8215164. It is already in rad/sec^2, correct? No conversions needed there?

Correct. You are computing Δω/Δt, so the units take care of themselves (since you already converted everything to standard units): (rad/s)/(s) = rad/s^2.

 

[tjohn101]

Correct. You are computing Δω/Δt, so the units take care of themselves (since you already converted everything to standard units): (rad/s)/(s) = rad/s^2.

Now there is one small problem. The answer is wrong. Would it be positive?

 

[Doc Al]

Now there is one small problem. The answer is wrong. Would it be positive?

The question is ambiguous as to sign, since no direction or sign convention was given. I would just give the magnitude of the acceleration.