Solving Motor Rotation: 0 to 1800rpm in 0.49s?

[fahraynk]

Homework Statement

The rotor of an electric motor weighs 10 pounds and is 4 inches in diameter. What is the length of time required for the motor speed to increase from 0 to 1800rpm, assuming a constant electrical torque of 20 in-lb and zero external load during this period? Assume the rotor is a homogeneous cylinder.

Homework Equations

The Attempt at a Solution

Moment of inertia (I) of cylinder according to google is $$I=1/2 MR^2 = 1/2*10*2^2=20\\\\\
1800 rpm = \frac{1800}{60} \frac{rotations}{second} * \frac{2\pi rads}{rotation} = 188.5\\\\
20*188.5=20t\\\\
t=188.5$$
The book says the answer is 0.49 seconds. I got 188.5 seconds. Which is correct?

 

[TSny]

0.49 s is correct.

Your overall approach is fine. But you are not giving enough consideration to the units of the various quantities. For example, the rotor weighs 10 pounds. But does M in the formula I = (1/2)MR² represent weight? You should rework the problem plugging in units for each quantity in the calculation. If the units in your calculation do not reduce to seconds when you solve for t, you know you made an error.

 

[haruspex]

0.49 s is correct.

Your overall approach is fine. But you are not giving enough consideration to the units of the various quantities. For example, the rotor weighs 10 pounds. But does M in the formula I = (1/2)MR² represent weight? You should rework the problem plugging in units for each quantity in the calculation. If the units in your calculation do not reduce to seconds when you solve for t, you know you made an error.

A slightly different take on the error... Not sure which is more helpful.

20 in-lb

The lb there does not represent mass. What does it represent?

 

[fahraynk]

I got it. There were 2 problems. They gave me weight but I thought it was mass, so I had to divide by gravity. The other was they gave me torque in inch pounds, I had to convert it to foot pounds. Thank you both.