Simple physics question: Which Spot on the wheel travels faster?

[lala_and_peril]

Homework Statement

Hello, I have difficulty understanding a problem on a practise mechanical aptitude test. I have a uploaded a photo of the question in case I am looking at it improperly. from what I understand, A and B are both making the same amount of rotations per minute, but A has to travel more distance to keep up with B, since it's a fixed object, therefore it's speed has to increase as well. I chose the answer A, but they said the answer is B (without an explanation). Can someone please explain to me why the answer is B?

Homework Equations

v=d/t

The Attempt at a Solution

 

[barryj]

I think the answer is A. Here is why. I assume the wheel is on a car for example. The bottom of the wheel where it is in contact with the ground does not move, it can be considered a pivot point. Now, when the tire rotates, Point A will move more than point B because it is further from the pivot point. I don't understand why the answer would be B. If the wheel is rotating about B, then A obviously moves faster.

 

[CWatters]

I think it's a very badly worded question. There are many ways to answer but I don't see how they get B either.

 

[462chevelle]

if you think of it in a gear ratio format it would be B because even if that is a dot. the circle "dot" has a smaller circumference so given the same amount of rpms the object with the smaller rollout would spin faster. say for example. the center dot is a 15 inch tire and the outer is a 30 inch tire. the 15 inch tire would spin faster given the same speed.

 

[barryj]

You must explain this better. I don't get your point.

 

[rcgldr]

If the wheel is rolling up or down the left side wall, and only the instantaneous speed is considered (versus the average speed per revolution), than at the moment shown in the diagram, B is moving faster than A.

Otherwise, if the average speed is to be considered, then if the wheel is rolling on a flat surface, B travels in a straight line while A follows the path of a curtate cycloid which is longer per revolution than a straight line, so the average speed of A is faster than B since it covers more distance in the same time period.

The problem statement doesn't clarify if instantaneous or average speed is to be considered, or if the wheel is supposed to be rolling on the left wall.

 

[462chevelle]

alright. you have a drag car with a 3.73 gear ratio with a 28 inch tall tire and say you cross the stripe at 5500 rpms. if you put a 30 inch tall tire you would lose + - .2 tenths in the gear ratio so it would be more like a 3.53 so therefore dropping your rpms, for arguments sake let's call it 300 rpms less across the stripe ignoring converter slip all else being equal. and B has a smaller ''tire'' than a. that's the way I interpret it.

 

[haruspex]

if you think of it in a gear ratio format it would be B because even if that is a dot. the circle "dot" has a smaller circumference so given the same amount of rpms the object with the smaller rollout would spin faster. say for example. the center dot is a 15 inch tire and the outer is a 30 inch tire. the 15 inch tire would spin faster given the same speed.

You have completely inverted the question. It shows a single wheel and asks which dot travels faster. Mere spinning is not travelling. You've reinterpreted it as two wheels with the same peripheral speed and ask which spins faster.

 

[462chevelle]

no. it should be the same concept as the further in on the wheel you get it would be spinning faster. how should I be interpreting it?

 

[utkarshakash]

The answer would be A here because B does not possesses an angular velocity wrt to CM of wheel. In case of A it has 2 velocities. One which is due to translational motion of the wheel in horizontal direction and the other which is due to rotational motion of the wheel directed along the tangent at point A. If we take out the resultant it would be definitely greater than velocity at B. As pointed out by rcgldr, the trajectory of A is a cycloid whereas for B it is a straight line.

 

[xxChrisxx]

no. it should be the same concept as the further in on the wheel you get it would be spinning faster.

the circle "dot" has a smaller circumference so given the same amount of rpms the object with the smaller rollout would spin faster.

Why? Just consider the physical consequence of what you propose with the two above statements.

It's obvious you know what's going on in real life, I think you've just got yourself in knots with how you are thinking about it. Haruspex is right, you are considering the reverse of the question.Also as it's written, the question is ambiguous. Is that all the information you are given?

 

[462chevelle]

does your interpretation of it make a the correct answer? because supposedly b is correct. instead I try to interpret it where b is correct. rather than come up with a reason its not. and if b is correct. why? if not the reason I stated.

 

[Borek]

Question should start with a definition of what it means by "travels faster". As it doesn't everyone uses their own definition, no wonder everyone gets a different answer.

 

[xxChrisxx]

does your interpretation of it make a the correct answer? because supposedly b is correct. instead I try to interpret it where b is correct. rather than come up with a reason its not. and if b is correct. why? if not the reason I stated.

If your interpretations leads you to a situation that doesn't occur in reality, then you discard it.
The reason for the difference is most likely average velocity vs instantaneous velocity. It's just an ill defined question.

no. it should be the same concept as the further in on the wheel you get it would be spinning faster.

This is very obviously wrong, as a wheel doesn't spin faster the closer you get to the centre (as you can assume it's rigid, even if it isn't it's certainly not flexible). Otherwise your rotational velocity at the hub axis would be infinte. Wheel turn with a single RPM.

What you did was take the same conempt we did. w = v/r
Rotational speed = tangential speed / radius.

You set tanential speed as constant (when the question stated that rotational speed was constant), which gives you the conclusion of b. This works if you have different sized wheels (ie different rolling radius), but not for different points on a given wheel.