Answer to Question #1904 in Mechanics | Relativity for nirmala

Question #1904
The angular position of a particle is given by theta(t) = b + ct + dt2, where b, c, and d are constants. The radial displacement of the particle is r (t) = a theta(t) where a is a constant. Determine (a) the angular velocity, (b) the angular acceleration alpha, (c) the linear velocity, (d) the transverse acceleration, and (e) the centripetal acceleration of the particle.
1
Expert's answer
2011-06-22T10:42:21-0400
a) The angular velocity, ω =dθ (t)/dt = c + 2d* t.
b) The angular acceleration, α = d ω /dt = 2d.
c) The linear velocity, v = dr/dt = a* dθ/dt = a( c + 2d*t.)
d) The transverse acceleration, at = dv/dt = a {2d}
e) the centripetal acceleration of the particle
ac = ω2*r = (c+2d*t)2*a*(b + ct + dt2) = 2a(c2+4cdt+4d2t2)*(b + ct + dt2) =
=2a(bc2 + tc3 + dct2 + 4dbct + 4dc2t2 + 4d2ct3 + 4d2bt2 + 4d2ct3 + 4d3t4)

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