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1. The problem statement, all variables and given/known data

ou are to find the coordinates of a pebble stuck in the tread of a rolling tire that is rotating counterclockwise (i.e., in the positive sense) with angular velocity w. The tire rolls without slipping on the ground (which is at y=0). The outer radius of the tire is R. At time t=0, the pebble is at the top of the tire, as shown.

(a)Find the velocity of the axle of the tire relative to a fixed point on the ground, [tex]\vec{V}[/tex]ag. Note the order of the subscripts: velocity of axle measured relative to the ground.

Express your answer in terms of R, w, and [tex]\hat{x}[/tex] and/or [tex]\hat{y}[/tex].

(b)Find the position vector of the pebble relative to the initial point of contact between the wheel and ground at a time t, [tex]\vec{r}[/tex]pg(t).

Express the position vector of the pebble in terms of R, w, t, and the unit vectors [tex]\hat{x}[/tex] and/or [tex]\hat{y}[/tex] of the xy coordinate system shown.

(c)Find [tex]\vec{V}[/tex]pg(t), the velocity vector of the pebble with respect to a fixed point on the ground, in terms of the unit vectors [tex]\hat{x}[/tex] and [tex]\hat{y}[/tex] of the xy coordinate system shown.

Express the velocity vector in terms of R, w, t, and [tex]\hat{x}[/tex] and/or [tex]\hat{y}[/tex].

(d)Now find [tex]\vec{a}[/tex]pg(t), the acceleration vector of the pebble with respect to a fixed point on the ground.

Express your answer in terms of R, w, t and [tex]\hat{x}[/tex] and/or [tex]\hat{y}[/tex] of the xy coordinate system shown.

2. Relevant equations

v = wR

atan = [tex]\alpha[/tex]/R

3. The attempt at a solution

Well part (a) i got which =

-(wR)[tex]\hat{x}[/tex]

The rest i need a little guidance on. Am i using the analogous equations of motion for rotational mototion? Or something different?

Any help would be great

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# Pebble in a rolling tire - finding velocity and acceleration

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