Insect on spinning record problem

In summary: I would use 262 cm.Keep in mind that the questioner used 1.5 cm/s, but the ant would travel 15 cm in 10 seconds at that speed, which is still a reasonable time to traverse the 15 cm, but it is not the 1 second that the questioner used.In summary, an insect crawls in a straight line from the edge to the centre of a spinning record at a speed of 1.5cm/s. This creates a spiral path that is approximately 262 cm in arc length, with 5.54 rotations completed during the walk. The record takes 1.85 seconds for a full rotation, with the last part of the spiral being a fraction
  • #1
lab-rat
44
0

Homework Statement


In an old record player, the flat round vinyl disc (record) is placed on a turntable which spins around. Once it gets going around and around, it moves so that the number of revolutions it makes per minute is constant (33 and 1/3). An insect settles on the edge of the spinning record. It decides to crawl in a straight line to the centre of the record.

a) draw the actual path the insect makes as seen by you the observer
b)If the insect moves from the edge to the centre (a distance of 15 cm) at 1.5cm/s, estimate the arc length of the path the observer sees.

The Attempt at a Solution



For a), the answer is obviously an arc. It would be ) if the disk is spinning clockwise correct?

As for b) I don't really understand. I can't seem to find the formula to be able to find the length of the arc. Since it definitely won't be in the shape of half of a circle, I can't use the formula for the circumference of a circle.. Any suggestions?
 
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  • #2
lab-rat said:

Homework Statement


In an old record player, the flat round vinyl disc (record) is placed on a turntable which spins around. Once it gets going around and around, it moves so that the number of revolutions it makes per minute is constant (33 and 1/3). An insect settles on the edge of the spinning record. It decides to crawl in a straight line to the centre of the record.

a) draw the actual path the insect makes as seen by you the observer
b)If the insect moves from the edge to the centre (a distance of 15 cm) at 1.5cm/s, estimate the arc length of the path the observer sees.

The Attempt at a Solution



For a), the answer is obviously an arc. It would be ) if the disk is spinning clockwise correct?

As for b) I don't really understand. I can't seem to find the formula to be able to find the length of the arc. Since it definitely won't be in the shape of half of a circle, I can't use the formula for the circumference of a circle.. Any suggestions?

Firstly it is a sad reflection to see my record player called "an old record player".

If the insect simply sat on the rim of the record for 1 minute, it would travel 33 1n 1/3 revolutions, an arc length 33 and 1/3 times the circumference of the circle.

At the speed given, the insect will take less than a minute to reach the centre, but still the record will have gone through several rotations.

For each rotation, the length of the spiral arc can be taken as the average of a circumference of the circle of largest radius and the circumference of the circle of smallest radius.

That should be enough information to get you going.
 
  • #3
So the circumference of the record is 94.25 cm, which means its arc length of the record is 3141.67 cm?

1 rotation would take 1.8 s so the insect would advance 2.7 cm per rotation right?

I'm sorry, I'm just really lost right now! I've been working on this number for way too long without any examples or explanations from the prof. I haven't done any physics in 2 years and that was at my french high school. All of the new terminology is really confusing so I am very sorry if I'm not catching on very quickly
 
  • #4
lab-rat said:
So the circumference of the record is 94.25 cm, which means its arc length of the record is 3141.67 cm?

1 rotation would take 1.8 s so the insect would advance 2.7 cm per rotation right?

I'm sorry, I'm just really lost right now! I've been working on this number for way too long without any examples or explanations from the prof. I haven't done any physics in 2 years and that was at my french high school. All of the new terminology is really confusing so I am very sorry if I'm not catching on very quickly

Those figures look appropriate.
By the end of 1.8 seconds, the insect is "on a circle" of radius 12.3 cm - which will have a smaller circumference. The spiral track it will have mapped out can be approximated to the average of the outer circumference and the inner circumference. Then there is the next "loop" of the spiral, and the next etc, then finally a fraction of the last "loop"
 
  • #5
Is this what you meant?

physics3.jpg


physics4.jpg
 
  • #6
lab-rat said:
Is this what you meant?

physics3.jpg


physics4.jpg

This looks good, except it looks like the last part of the spiral is only part of a full rotation.
The ant was 1.5 cm from the centre, so took only 1 second to get there. The record takes 1.85 seconds for a full rotation, 1 second is only 1/1.85 of the full spiral so I would be multiplying that last 4.71 cm by 1/1.85.

Just as an aside - you could have done it in one go.
In all there is 5.54 rotations done during the walk.
Large circle is the record, r = 15
small circle is the centre, r = 0

answer is 5.54 * 2pi * (15+0)/2 which gives the answer you will get once you adjust for that last part "circle".
 
  • #7
I fixed it and ended up with 261.81 which is pretty close to the answer.
How should I formulate my answer? Is Arc length = 261.81 cm appropriate?

Thank you so much for your help by the way, very much appreciated!
 
  • #8
lab-rat said:
I fixed it and ended up with 261.81 which is pretty close to the answer.
How should I formulate my answer? Is Arc length = 261.81 cm appropriate?

Thank you so much for your help by the way, very much appreciated!

The questioner referred to this spiral path as an arc length, so to call it an arc length is appropriate. best to use their term even if it is wrong.

You have to be careful how you round off any values on the way through the problem.
When I don't round off until the final answer I get 261.799 or 261.8 cm
 

Related to Insect on spinning record problem

1. What is the "Insect on spinning record problem"?

The "Insect on spinning record problem" is a physics thought experiment that explores the concept of rotational motion and centripetal force. It involves a hypothetical scenario where a small insect is placed on the edge of a spinning record and must move towards the center without slipping off due to the record's rotation.

2. What factors affect the outcome of the "Insect on spinning record problem"?

The outcome of the "Insect on spinning record problem" is influenced by several factors, including the speed of the record's rotation, the friction between the insect and the record, and the insect's weight and size. These factors determine the centripetal force acting on the insect and whether it will successfully move towards the center or slip off.

3. How does centripetal force play a role in the "Insect on spinning record problem"?

Centripetal force is the force that acts towards the center of a circular motion and keeps an object moving in a circular path. In the "Insect on spinning record problem," the centripetal force is responsible for the insect's movement towards the center of the record, as it counteracts the centrifugal force that tries to push the insect off the record due to its rotation.

4. Can the "Insect on spinning record problem" be applied to real-life scenarios?

Yes, the principles of the "Insect on spinning record problem" can be observed in various real-life scenarios, such as the movement of cars on curved roads, the rotation of amusement park rides, and the behavior of objects in orbit. It is a fundamental concept in physics and has practical applications in many fields, including engineering and astronomy.

5. How does the "Insect on spinning record problem" relate to angular velocity?

Angular velocity is a measure of how quickly an object is rotating around a fixed point. In the "Insect on spinning record problem," the angular velocity of the record affects the insect's ability to move towards the center, as a higher rotation speed results in a stronger centripetal force. This relationship is demonstrated by the equation v = ωr, where v is the linear velocity, ω is the angular velocity, and r is the distance from the center of rotation.

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