To find the velocity and acceleration vectors for uniform circular motion and to
ID: 1531504 • Letter: T
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