angular quantity

You 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
圖片參考：http://session.masteringphysics.com/render?var=omega
. The tire rolls without slipping on the ground (which is at

圖片參考：http://session.masteringphysics.com/render?tex=y+%3D%0A0

). The outer radius of the tire is
圖片參考：http://session.masteringphysics.com/render?var=R
. At time

圖片參考：http://session.masteringphysics.com/render?tex=t+%3D+0

, the pebble is at the top of the tire, as shown.
(Intro 1 figure)


圖片參考：http://imgcld.yimg.com/8/n/HA00021001/o/700911050032113873406410.jpg


1)Find the velocity of the axle of the tire relative to a fixed point on the ground,
圖片參考：http://session.masteringphysics.com/render?var=v_vec_ag%28t%29
. Note the order of the subscripts: velocity of axle measured relative to the ground.
Express your answer in terms of
圖片參考：http://session.masteringphysics.com/render?var=y_unit
.
The pebble and tire have now rolled as shown in the figure.
(Intro 2 figure)
Answer the following questions for
圖片參考：http://session.masteringphysics.com/render?tex=t%3E0
.


圖片參考：http://imgcld.yimg.com/8/n/HA00021001/o/700911050032113873406411.jpg


2)Find the position vector of the pebble relative to the initial point of contact between the wheel and ground at a time
圖片參考：http://session.masteringphysics.com/render?var=r_pg_vec%28t%29
.
Express the position vector of the pebble in terms of
圖片參考：http://session.masteringphysics.com/render?var=y_unit
of the xy coordinate system shown.
3)Find
圖片參考：http://session.masteringphysics.com/render?var=y_unit
of the xy coordinate system shown.
Express the velocity vector in terms of
圖片參考：http://session.masteringphysics.com/render?var=y_unit
.
4)
Now find
圖片參考：http://session.masteringphysics.com/render?var=a_vec_pg%28t%29
, the acceleration vector of the pebble with respect to a fixed point on the ground.
Express your answer in terms of
圖片參考：http://session.masteringphysics.com/render?var=y_unit
of the xy coordinate system shown.