This preview shows pages 1–6. Sign up to view the full content.

Chapter 7 Additional Notes In this chapter we are considering rotational motion. To do so we can consider a solid object which is rotating about a fixed axis

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
In general this is at least a two dimensional problem, so we would have to know how the position of the object is changing over in each direction. Hence we would need to know the velocity of each direction independently. Then to find the distance traveled we would have to essentially use the Pythagorean theorem. Graphically that means we are considering
Δ x Δ y Δ s Δ y Δ x Δ s = Δ x ( ) 2 + Δ y ( ) 2 Mathematically written as

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
However, this is only good for small changes, since the displacement s is a straight line. This means that for large changes using this method will not give us the correct displacement. To get the correct distance we would need to use calculus. However since this is beyond the scope of this course, we will use a different method. Since the object is rigid, that means that during a given time, each piece of the object will under go the same rotation. This means that each piece will be rotated by the same angle.
So we can then use the angle to define the distance the object travels, using the arc length. Since we are only using one piece of information, that

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.