Calculating Torque for a LP Turntable

[agadag]

Homework Statement

An LP turntable must spin at 3.52 rad/s to play a record. How much torque must the motor deliver if the turntable is to reach its final angular speed in 1.7 revolutions, starting from rest? The turntable is a uniform disk of diameter 30.8 cm and mass 0.26 kg.

Homework Equations

T= I * angular acceleration(a)

The Attempt at a Solution

-converted rev to rad
- found time from avg ang vel and distance
-used that to calculate acceleration
nothings working. I have tried every possible way. Someone please work out the problem so I can understand how to do this. THANK YOU! I WILL BE SOOOO GRATEFUL. I am ready to cry!

 

[Delphi51]

found time from avg ang vel and distance

This step doesn't sound right. You are given the turning angle to get to a rotational speed - like being given the distance for a racecar to get up to 100 km/hr. You would probably use Vf² = Vi² + 2ad to find the acceleration in the linear problem, so you would do the rotational problem with the rotational analog of that formula and find the angular acceleration, from which you can easily get the torque.

 

[agadag]

you are right. I found the eqn :
w=ang velocity
@-ang accelration
theta - angle

w²_f = w_i² + 2@theta.
how do i find theta?

 

[Delphi51]

Subtract wi² from both sides. Then divide both sides by 2 theta.

 

[agadag]

ummm...
I multiplied the diameter (after converting into m) by 2 pie, in order to get theta. then i solved for angular acceleration in order to find torque in the eqn:
Torque = Impulse * angular acceleration.
however this didn work for me either...
sooo I am lost...

 

[Delphi51]

Sorry, misunderstood! You are given that the final angle is 1.7 revolutions and just need to convert this to radians. 1 revolution = 2π radians.
Solve the equation for angular acceleration.

 

[agadag]

Sorry, misunderstood! You are given that the final angle is 1.7 revolutions and just need to convert this to radians. 1 revolution = 2π radians.
Solve the equation for angular acceleration.

Already tried that. I got
10.68²=3.52²+ 2*angaccel*193.5 (multiplying diameter by 2pie)
solving for ang accelration, i got ...26.25 ...which is wrong...

 

[Delphi51]

10.682=3.52^2+ 2*angaccel*193.5 (multiplying diameter by 2pie)

I don't see that! wf = 3.52 and when you square it, you don't get 10.682.
wi = 0. You must not multiply by diameter to get the angle - an angle does not have any length units; should be just in radians.

To make your work clear, maybe write the formula first, then sub in the numbers without using a calculator so we can see how you got your numbers.

 

[agadag]

1.72 rev= 10.68rad
Im confused..? The problem says that final speed should b 1.72 n ur right about the initial speed.

 

[agadag]

SOoo...
10.68²= 0 + 2*ang acc * .308 m
114= .616angaccl
185.06=ang accl?

 

[agadag]

yea I am still not getting the right answer for torque...

 

[Delphi51]

wf² = wi² + 2αθ
α = (wf² - wi²)/(2θ)
= 3.52²/(2*1.7*2*π)

 

[agadag]

that gives me an angular accelration of .580
using that to find Torque:
T = F (r)
= MA (r)
=.26 *.589 8.154
=.023?
ahhhhh what am i doing wrong?? :(

 

[Delphi51]

You said initially that torque = I*α.
Do you know how to find the moment of inertia I for the turntable?
Wikipedia has a list of all the moment of inertia formulas in their article of that name. No doubt you have them in your textbook, too.

 

[agadag]

I tried doing it both ways. I am so confused as to which formula to use. But i believe i know how to find moment of inertia. I used the formula I =mr² and then multiplied that with acceleration n still got the wrong answer...

 

[Delphi51]

Sorry, I = mr² applies only to a ring. Your turntable is a solid cylinder or disk. Look up the appropriate formula for I here:
http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html#mi
(scroll down to the pictures and formulas).

You are almost finished. Just calculate I, then use torque = I*α.
Your value of angular acceleration is correct.

 

[agadag]

Thanks a bunch!