What is the displacement?

A disc of perimeter 4pi is rolling. What is the displacement between the point of contact and ground after a quarter of a revolution.(Didn't mention initial point of contact)

#Mechanics

Easy Math Editor

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Comments

The start position of the red point is:

$(x,y) = (0,0)$

The end position of the red point is:

$(x,y) = \Big( \Big( \frac{\pi}{2} - 1 \Big) R,R \Big)$

The displacement is:

$D = R \sqrt{\Big( \frac{\pi}{2} - 1\Big)^2 + 1}$

In this particular case, $R = 2$ , so:

$D = 2 \sqrt{\Big( \frac{\pi}{2} - 1\Big)^2 + 1}$

Steven Chase - 1 year, 11 months ago

But I thought that the displacement between the point of contact and ground would be the same anytime because I didn't say the the displacement of initial point of contact and ground. Anyhow, thanks for replying

Jyothiraditya Chaitanya - 1 year, 11 months ago

If you want the displacement of the present point of contact, it should just be $\frac{\pi}{2} R$ , or $\pi$ in this case

Steven Chase - 1 year, 11 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$