physics fun

[clanthar]

Thought you'd all enjoy this.

Still sitting here going through yesterday's bike race photos. I noticed a nice little photo proof of some basic physics in this shot:

I positioned myself for the light but also on the uphill end of the course where these guys slow down below 30 mph. For the sake of this illustration let's assume they were moving at 25 mph when I tripped the shutter.

Note the leader's front tire. He has ZIPP brand tires and the logo on the tire is right at the pavement. Notice the difference in sharpness in the tire. Here's an enlargement:

If the forward speed of the bike is 25 mph then the speed of the tire in contact with the pavement is 0 mph while the speed of the top of the tire is 50 mph. The back of the tire is accelerating toward the top and the front of the tire is decelerating toward the bottom. You can see that the photo proves this nicely (shutter speed was 1/1250 sec).

Take Care,
Joe

 

[peanut170]

But if you look at the shadow of the left brake this just voids you're whole theory, nice try though.

 

[Josh66]

Why would three different points on the same tire be moving at different speeds...?

I don't know ... I never really took any high level physics classes, but that just doesn't make sense to me...

If you had a round object (a tire), spinning at a relatively constant RPM, I don't see how any two points on the perimeter of the tire could have different speeds...

 

[astroskeptic]

Why would three different points on the same tire be moving at different speeds...?

I don't know ... I never really took any high level physics classes, but that just doesn't make sense to me...

If you had a round object (a tire), spinning at a relatively constant RPM, I don't see how any two points on the perimeter of the tire could have different speeds...

It is because of the differing frames of reference. From the frame of reference of the wheel axle, your logic applies: the top of the tire is moving with velocity v forward and the bottom is moving with velocity v backward. However, the axle itself also happens to be moving forward with velocity v in the frame of reference of the ground (which is the same frame as the camera). So, what are the wheel velocities from the frame of reference of the ground? They are the axle-frame values plus the offset going from the axle frame to the ground frame: top=v+v=2V, bottom=-v+v=0 (axle would be 0+v=v).

 

[Ryan L]

Hmm I am just confused on how you stopped motion of the bottom of the tire and not the top. i don't think its a matter of sharpness unless you blurred the other parts. I am not a physics guy either though so I buy your theory. Thanks for the lesson.

 

[Ryan L]

Why would three different points on the same tire be moving at different speeds...?

I don't know ... I never really took any high level physics classes, but that just doesn't make sense to me...

If you had a round object (a tire), spinning at a relatively constant RPM, I don't see how any two points on the perimeter of the tire could have different speeds...

It is because of the differing frames of reference. From the frame of reference of the wheel axle, your logic applies: the top of the tire is moving with velocity v forward and the bottom is moving with velocity v backward. However, the axle itself also happens to be moving forward with velocity v in the frame of reference of the ground (which is the same frame as the camera). So, what are the wheel velocities from the frame of reference of the ground? They are the axle-frame values plus the offset going from the axle frame to the ground frame top=v+v=2V, bottom=-v+v=0.

I read it and felt like this......then re-read it and started feeling educated:study:......tried pounding that info into my head....:banghead:....and now look what you did!:madmad:

 

[Josh66]

Why would three different points on the same tire be moving at different speeds...?

I don't know ... I never really took any high level physics classes, but that just doesn't make sense to me...

If you had a round object (a tire), spinning at a relatively constant RPM, I don't see how any two points on the perimeter of the tire could have different speeds...

It is because of the differing frames of reference. From the frame of reference of the wheel axle, your logic applies: the top of the tire is moving with velocity v forward and the bottom is moving with velocity v backward. However, the axle itself also happens to be moving forward with velocity v in the frame of reference of the ground (which is the same frame as the camera). So, what are the wheel velocities from the frame of reference of the ground? They are the axle-frame values plus the offset going from the axle frame to the ground frame: top=v+v=2V, bottom=-v+v=0 (axle would be 0+v=v).

I think I get it now... Interesting.

:thumbup:

 

[supraman215]

could be because the bike is moving left, right as he pedals, towards and away from the camera. That would explain why the bottom is crisp. The whole wheel is spinning at the same speed.

 

[Josh66]

Just to make sure I'm seeing this right...

If the bike was on a jack or something, what I said earlier would be true, right? All points (equal distance from the axle) would be moving at the same speed...?

But because the ground and axle are both 'moving', the 'sides' are moving faster?

Should the speed of the part of the tire directly above the axle be the same as the speed of the part directly below it?

(Why doesn't the ground exhibit the same blur?)




(Physics noob ... but always interested in it...)


edit
I can't help but see this as the same as measuring propeller tip speed... (Which may be totally wrong for this case.)
I think if the wheel were suspended somehow, it would be the same as measuring prop tip speed though... right?
(If you know the RPM and the prop diameter, you can figure out the tip speed, which is good to know for multiple reasons...)

 

[Stephen.C]

Wow, this is crazy! This reminds me I have to do my physics HW for tomorrow heh!

 

[robitussin217]

Wow, this is very interesting. I think the blur of the spokes shows it better than the lettering on the tires.

How does panning affect the ability to see the effect? You could take a bike and paint white dots on the tires, take a shot and compare the length of the blur and then try the same shot, panned.

 

[astroskeptic]

O|||||||O,

Your intuition is right but you're not quite getting the concept of frame of reference.

If the bike was on a jack, then you're right: all parts of the tire equidistant from the axle are moving at the same speed. This view of the world is what I call the axle frame of reference. Even if the bike is moving, this is still true: from the point of view of the axle, the parts of the tire are moving with a constant speed.

But the axle's point of view is not the same as the camera's when the bike is moving (although it is when the bike is stationary on the jack).

To understand how the camera weeks the tire, we must translate from the axle frame of reference to the camera's. Since the camera is stationary on the ground, it is the ground's frame we need. The difference between the ground's frame and the axle's frame is a constant speed corresponding to the speed of the bike over the ground. This just happens to be the same speed as that of the outermost part of the wheel. We add the speeds as I showed above to get the ground frame speeds.

Note that the ground is moving from the frame of reference of the axle, but not the camera which is why we would not expect motion blur on anything stationary from the frame of reference of the ground (which would only include the bottom of the tire).

 

[astroskeptic]

The circular motion in this example makes the intuition here harder to develop.

Consider a simpler case: a bus with a single passenger. Suppose the bus is moving to the right at speed v and we're shooting the passenger through the windows. Clearly, to the camera the passenger is moving right at speed v and we'll get motion blur.

Now, from the passenger's frame of reference, she isn't moving. Suppose she gets up and heads left toward the back of the bus (i.e. left) at a speed v relative to the bus seats.

What would the camera see? The passenger would appear stationary because the leftward motion inside the bus would exactly cancel the rightward motion of the bus itself and we'd expect no motion blur on the passenger (we'd get a sharp passenger and motion blurred bus). The -v (left) speed of the "inside the bus" frame of reference added to the +v (right) speed of the bus in the ground frame gives us -v + v = 0 speed relative to the ground.

 

[Josh66]

Yeah, that concept is pretty familiar to me...

Say a missile (whatever kind you want) has a velocity of mach 3 if fired from the ground. It's on a plane traveling at mach 1. The pilot fires the missile, it leaves the plane at mach 4.

Correct?

 

[Vinny]

Took Physics over 25 years ago and it's a little fuzzy but there are 2 different velocities happening - angular velocity (tire spinning) and forward velocity (bike moving forward), leave the side to side motion at 0 velocity.

Angular velocity is constant throughout the tire or the tire would deform if it were stopped for any length (or fraction) of time. The whole bike is moving at a constant speed forward so that has no bearing.

I believe what your seeing is the top of the tire is at a slightly different angle than the bottom in relation to the camera and that is what is giving the blurred words. I think if the photo was taken perpendicular to the tire all 3 words would be clear.

Of course I may be totally wrong!