Does circular motion affect different points on a car's wheels differently?

[SemperFiKandJ]

I have a few questions...okay lots actually! I am terribly confused and hopefully you can help me!

A car is up on a hydraulic lift at a garage. The wheels are free to rotate, and the drive wheels are rotating with a constant angular velocity. Does a point on the rim of a wheel have a.) a tangential acceleration and b.) a centripetal acceleration?

Two points are located on a rigid wheel that is rotating with an increasing angular velocity about a fixed axis, The axis is perpendicular to the wheel at its center. Point 1 is located on the rim, and point 2 is halfway between the rim and the axis. At any given instant which point if either has a greater a) angular velocity b) angular acceleration c) tangential speed d) tangential acceleration and e) centripetal acceleration?

A building is locating on the Earth's equator. Which has the greatest tangential speed due to the Earth's rotation, the top floor, the bottom floor, or neither?

 

[dextercioby]

What are your thoughts?

Daniel.

 

[SemperFiKandJ]

I am going in circles with these! I seriously have read the book, and my brain is just broken! I am thinking that a and b for the first question are both yes, but I honestly do not know why! I don't even know where to start to be honest, I am sure if I get started I can finish it!

 

[dextercioby]

Nope.The answer to the first question (a) from 1 is NO.Why?HINT:the angular velocity is constant...

Daniel.

 

[Theelectricchild]

For the first problem: "constant angular velocity" is all the clue you need for this... what do you know about uniform circular motion? That is, first of all IS THERE an acceleration? And if there is, what direction does it point when the object travels with CONSTANT speed? That is, how many vectors would you need to draw when for a constant speed case? Then decide how many you'd draw if the wheels were speeding up.

You would do well to find diagrams in your text that show what centripetal and tangential acceleration vectors look like.

 

[SemperFiKandJ]

So if angular velocity is constant there won't be a tangential acceleration, but there will be centripetal acceleration? Because velocity and acceleration are both vectors, I thought they had a direct relationship! Maybe I don't understan the difference between centripetal and tangential accelerations! Isn't tangential a linear line from a point in a circle, and centripetal just the circle?

 

[Theelectricchild]

You are indeed correct, however you are confusing angular velocity with the normal velocity vectors you've probably been dealing with...

Angular velocity is described by a pseudovector designated by a right hand rule... in this simplistic case, you need the information only to know that the wheel is spinning without speeding up or slowing down...

With that in mind, there is indeed a tangential velocity vector associated at the points along the wheel, but the acceleration vector points toward the center. The reason why it always points to the center is that the direction of the velocity vector (thats TANGENTIAL) is changing at a CONSTANT rate... that is, just because the magnitude of the vector isn't changing, an acceleration occurs from the simple fact that the direction is... furthur butressing the fact that velocity can never ever be treated as a scalar.

 

[Theelectricchild]

I admit, it's really difficult to, at first, accept the fact that even though acceleration points toward the center of the circle, why is it that things are not pulled toward the middle... ? You'll hopefully cover this phenomenon soon enough.

 

[SemperFiKandJ]

I am sorry! I think I am physics retarded! I am totally confused now! Maybe I am trying to make it more simple then it really is! What about the other two? Along the same lines? Any hints?

 

[Theelectricchild]

Ok so for problem 2 part a which point has a greater angular velocity?

Well, I hope that your professor has shown you this general equation

$$\omega=\frac{v}{r}$$

Well let's take a look at it! The point at the outter part of the wheel at the rim... its covering more distance in a lesser amount of time than the inner point right? So what quantity in the aforementioned equation does the outter point have more of? In addition, what other quantity does it have more of than compared to the inner point? You will end up comparing two ratios--- are they equal?

 

[Theelectricchild]

Let's attack part b:

angular acceleration

Well let's see here, you need to understand what tangential acceleration is to really know this...

I hope your professor has gone over the general equation

$$\alpha=\frac{a_t}{r}$$

Now let's take a look at that... the wheel is spinning faster and faster right? we know that the tangential accelerations are simply the rate of change of the tangential velocities of the two points... even though the tangential velocity of the outer point is greater than the inner, is the rate at which it's changing any different? I think you can answer the question if you know that!

 

[Theelectricchild]

Part c and d should be a breeze after understanding part a and b. But what about part e? Centripetal acceleration!

Well I hope your professor has gone over the general equation

$$a_c=\frac{v^2}{r}$$

now with this, we know that the outter point has a greater velocity correct? We also know that it has a greater radius --- but look at that! v is SQUARED! It's a matter of precedence, who beats out who! ?

 

[SemperFiKandJ]

Ahhh! I am pulling out my hair! I am going to give these all a shot! Thank you for your help! I might have more questions, but not tongiht! Definitely tomorrow!

 

[Theelectricchild]

No problem--- I remember my first physics class was quite scary--- just keep at it, it will come with practice and reading.


And this website :D jk.

 

[Theelectricchild]

I know this is a bit late probably, but you can use that same analysis to answer: Which has the greatest tangential speed due to the Earth's rotation, the top floor, the bottom floor, or neither?