Calculating Time for Turntable Platter to Stop at 0rpm

[utility_belt]

Hi all,

I haven't studied rotational physics in a long time so this may be a stupid question, but here goes. I'm trying to model the properties of a turntable (record player). Using the theories of rotational motion, is it possible to calculate the time it would take for the spinning turntable platter to come to a complete stop when the power to the motor is cut?

Given that I know the starting velocity is 33 rpm, the final velocity is 0rpm and the weight of the platter is 1.996kg is it possible to calculate the time it takes to come to a complete stop?

Thanks for you help!

 

[Chen]

Yes, but you would need to know the coefficient of friction between the turntable and the platter. If there were no friction, the platter would never stop. Once you have the magnitude of the friction force you can find the angular deceleration of the platter and how long it would take for its angular velocity to become 0.

 

[utility_belt]

Ah yes, I thought that would be the missing factor. I assume this (the friction between the turntable and the platter) is something that is not so easy to measure/calculate?

 

[Michael D. Sewell]

If you can find such a turntable, it is very easy to calculate. Just measure how much force it takes to turn it. All you need is a small scale.

The other thing you could do is to time how long it takes to come to a stop. With a little algebraic manipulation you can solve the equation for the coefficient of friction.

Or you could guess. Maybe around .1 ? Does it have bearings?
-Mike

 

[Chen]

$$V(t) = V_0 + at$$
In our case the platter stops so V(t) is zero:
$$t = -\frac{V_0}{a}$$
(a will also be negative so the time will be positive.)

Finding a is just a matter of: (fk being kinetic friction)
$$\Sigma F = ma = -f_k = -N\mu = -mg\mu$$
$$a = -g\mu$$

Plug that into the formula above:
$$t = \frac{V_0}{g\mu}$$
And you're done.
Or if you have the time and want to find the coefficient of friction:
$$\mu = \frac{V_0}{gt}$$

 

[utility_belt]

OK,

Thanks Chen. I've measured the time it takes for the turntable to stop, and get an average of about 15 seconds. I'm trying to put that into your last formula, to find the coefficient of friction but am unsure of a couple of variables.

V(0) Velocity is 33.33 rpm so = 3.49 rad/s
t Time is = 15s

So that would make: Coefficient = 3.49 / (g * 15)

Stupid question, what is g?
Thanks.