Vectors: wheel w/ radius r rolloing to right along x-axis w/ constant speed v....

[red112]

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[stapel]

The diagram shows a wheel of radius r rolling to the right along the x -axis on horizontal ground, with its centre moving at constant speed v. Relative to O as origin, the position vector of a point A on the rim of the wheel at time t after leaving the origin is given by the expression r = vt i + r sin(wt) i + r j + r cos(wt) j, where w is the angular speed of rotation around the centre of the wheel.

In the diagram, the angle wt is measured clockwise starting from the vertical. If the wheel is to roll without slipping, then any point such as A must be momentarily at rest when it touches the ground.

1. Show the development of the expression for the position vector of A.

2. (a) Use a spreadsheet or other technology to produce a graph showing the actual path of A as the wheel rolls. (This would be the path seen by an observer at night if point A was somehow illuminated.)

(b) Show mathematically that point A never moves to the left.

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Have no idea how to do the questions above, any help would be greatly appreciated.

Are you saying that you missed the chapter on vectors, so you're needing lesson instruction on the topic? Thank you!

 

[red112]

Are you saying that you missed the chapter on vectors, so you're needing lesson instruction on the topic? Thank you!

i went to a new school and they had already covered this topic where i had not, so i am very confused on these questions

 

[stapel]

i went to a new school and they had already covered this topic where i had not, so i am very confused on these questions

It sounds like you're needing private instruction, so you can get caught up to the class. Unfortunately, we cannot here provide the weeks or months of classroom instruction that you've missed. If the school isn't providing assistance, then you may want to consider hiring a qualified local tutor and setting aside an hour or two a day for intensive personalized instructions.

(I grew up being in your position every year or two, when we'd move again. It's not fun!)

Good luck!