# For pure rolling , Proof for every point on wheel has velocity = vc + wr

There are 2 texts I have seen for every point on wheels finding out the exact velocity of certain points.

The theory states for all is that : Every point on wheel has total v = rotational + translational.

Way 1 )

Here , we consider axis of rotation as the bottom point of wheel which is also knows as instantaneous axis of rotation.

Then , v = $$2r*w$$ for top point of wheel.

Q1 : Does it mean to say 2r*w = rotational + translational. If yes , can we find their individual values.

Way 2)

Every point on the wheel has v = vc ( V of centre of mass ) + Vr ( V rotational due to rotation of body about its centre ).

I searched a lot to see if there is any derivation for this but I couldn’t find it. Also , here. Axis of rotation instead of bottom is centre of wheel which is different from the way 1.

Q2: If you could help with the derivation of it ?

The point is. I really want to understand it. I’m extremely sorry for previous follow up Q similar to it.

• What's the difference between this and your previous question? Dec 18, 2021 at 10:48
• @Transistor The point is , I feel the users are not getting what I’m trying to ask. Maybe I’m unclear with my Q . So , I feel this one is more direct. That’s all. Dec 18, 2021 at 10:54
• I'd be afraid that it will be flagged as a duplicate. Recommendation is to fix the original question. Dec 18, 2021 at 11:01
• Go back to the original, do the little proof yourself and think about it. Instead of marking two points, you can only mark one on the disk, and the start point on the desk, then roll the disk until the point gets in touch with the desk, mark the second point on the desk. Now measure the distance between the two points on the desk, this is the distance traveled in one full revolution. If you have clocked the start and end time, you got both RPM and linear velocity.
– r13
Dec 18, 2021 at 11:53
• Also note, "A Point" has no velocity if stays in the same position. Velocity is a measure of change in distance within a time interval, whether the distance is measured radially or linearly, the distance traveled is the same for both.
– r13
Dec 18, 2021 at 12:09