Answer to Question #1904 in Mechanics | Relativity for nirmala

Question

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.

Answer 1

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)