How Far Can a Coin Be Placed on a Rotating Record Without Slipping?

In summary, the question asks for the maximum distance a coin can be placed from the center of a rotating record before slipping off, given a coefficient of static friction and rotation rate. The solution involves setting the force due to friction equal to the centripetal force and solving for the distance. The correct answer is 0.08 meters, which can be found by converting the rotation rate to radians per second and correcting a conversion error.
  • #1
pucr
8
0

Homework Statement


A small coin is placed on a record that is rotating at 33.3 rpm. If the coefficient of static friction between the coin and the record is 0.1, how far from the center of the record can the coin be placed without having it slipped off?


Homework Equations


w = 33.3 rpm = 1.11 rad/sec
Force due to friction = Centripetal force


The Attempt at a Solution


I tried this...
Force due to friction = .1mg = .98m
Centripetal force = ma = m((r*w^2)/r) = mrw^2 = 1.2321mr
soo...
.98m = 1.2321mr
=> .98 = 1.2321r
=> r = .795 m

Unfortunately, the answer should be .08 meters.
I thought at first that I messed up a decimal place somewhere but I can't see where. :-\
I may be going insane...
 
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  • #2
Welcome to PF.

What acceleration will the coin tolerate without slipping?

If the coefficient of friction is u and the mass is m then

u*m*g = m*v2/r

v = w*r =2*π*f*r

u*g/w2 = r = u*g/(2*π*f)2
 
  • #3
pucr said:

Homework Equations


w = 33.3 rpm = 1.11 rad/sec
Fix that conversion.
 
  • #4
ooh thanks.
It should be 3.487 rad/sec making the answer .0806 meters
 

Related to How Far Can a Coin Be Placed on a Rotating Record Without Slipping?

1. What is friction on a rotating record?

Friction on a rotating record refers to the resistance or force that is created when the record is spinning against the stylus or needle, which can affect the sound quality and playback of the record.

2. How does friction affect the sound quality of a record?

Friction on a rotating record can cause a scraping or scratching sound, known as surface noise, which can distort the original sound of the record. It can also cause wear and tear on the record and the stylus, leading to decreased sound quality over time.

3. How can I reduce friction on a rotating record?

To reduce friction on a rotating record, you can make sure that the record is clean and free of dust and debris. You can also use a good quality stylus and make sure it is properly aligned with the record. Additionally, using a record clamp or weight can help keep the record in place and reduce friction.

4. Can friction on a rotating record damage the record?

Yes, friction on a rotating record can cause damage to the record over time, as it can create scratches and wear on the surface of the record. This can also lead to decreased sound quality and potentially make the record unplayable.

5. Is there a way to measure the amount of friction on a rotating record?

Yes, there are devices such as a tracking force gauge that can measure the amount of friction between the stylus and the record. This can help ensure that the stylus is properly aligned and not causing excessive friction on the record.

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