To find the velocity and acceleration vectors for uniform circular motion and to

Question

To find the velocity and acceleration vectors for uniform circular motion and to recognize that this acceleration is the centripetal acceleration. Suppose that a particle's position is given by the following expression r vector (t) = R [cos(omega t)i + sin (omega t)j] = R cos (omega t)i + R sin (omega t) j What type of motion does this represent? Using dimensional analysis, what units does w have? Find the particle's velocity as a function of time. Find the particle's acceleration as a function of time.

Explanation / Answer

r(t) = R*cos(wt)i + R*sin(wt)j

That use in find all answer

a) Motion is circular

b) the unit of w is s^-1

c) v(t) = r'(t) = -Rw*sin(wt)i + Rw*cos(wt)j

d) a(t) = v'(t) = -Rw^2*cos(wt)i - Rw^2*sin(wt)j

e) Magnitude of v(t) = v = sqrt[(-Rw*sin(wt))^2 + (Rw*cos(wt))^2] = Rw

f) Magnitude of a(t) = a = sqrt[(-Rw^2*cos(wt))^2 + (-Rw^2*sin(wt))^2] = Rw^2

g) a = Rw^2 = v*w

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