Angular motion
Not what you're looking for?
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 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, v_pg(t) . Note the order of the subscripts: velocity of axle measured relative to the ground. Express your answer in terms of R, w,t and unit vectors x and/or y
b)Find the position vector of the pebble relative to the initial point of contact between the wheel and ground at a time t, r_pg(t). Express the position vector of the pebble in terms of R,w ,t , and the unit vectors x and/or y of the xy coordinate system shown.
c)Find v_pg(t), the velocity vector of the pebble with respect to a fixed point on the ground, in terms of the unit vectors and of the xy coordinate system shown. Express the velocity vector in terms of R,w ,t , and unit vectors x and/or y.
d)Now find a_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 x and/or y of the xy coordinate system shown.
Purchase this Solution
Solution Summary
The solution contains 3 pages including full derivations and graphs.
Solution Preview
Hello and thank you for posting your question to Brainmass!
The solution is attached ...
Purchase this Solution
Free BrainMass Quizzes
Classical Mechanics
This quiz is designed to test and improve your knowledge on Classical Mechanics.
Introduction to Nanotechnology/Nanomaterials
This quiz is for any area of science. Test yourself to see what knowledge of nanotechnology you have. This content will also make you familiar with basic concepts of nanotechnology.
Variables in Science Experiments
How well do you understand variables? Test your knowledge of independent (manipulated), dependent (responding), and controlled variables with this 10 question quiz.
Intro to the Physics Waves
Some short-answer questions involving the basic vocabulary of string, sound, and water waves.
Basic Physics
This quiz will test your knowledge about basic Physics.