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Circular motion: Rolling of a wheel

Q- The position vector of a particle moving on the rim of a rolling wheel in the x-y plane is given by

r = (10t + 5 cos 2t) i + (5 - 5 sin 2t) j, here r is in meters and t is in seconds. i and j are unit vectors in x and y directions respectively.

(a) What are the velocity and speed of the particle as a function of time?

(b) Sketch the path that the particle traces out as the wheel rolls along.

(c) Find the x-values for which the particle is in contact with the surface upon which the wheel rolls.

(d) What is the acceleration of the particle?

(e) At what times is the particle not moving, and where is the particle on the rim related to the horizontal surface at these times?


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