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Kinematics of a Particle in a Plane (using polar description)

Example: Particle, P, starts in motion from the origin and moves along a path described by the

parabola shown in the figure below. The constant x-component of velocity is dx/dt = 3 ft/sec.

Find the radial and transverse components of velocity and acceleration of particle, P, at

the point where (x,y) = (1,1).

Strategy: First calculate the x and y components of velocity and acceleration of P at (1,1).

Then calculate the unit vectors in the radial and transverse directions.

Note: dy/dt = 2x dx/dt = 2(1)(3) = 6 and d²y/dt² = 2(dxdt)² + 2x d²x/dt² = 2(3²) + 2(1)(0) = 18

v_P = 3i + 6 j ft/sec and a_P = 18 j ft/sec²

Start by showing the polar description (r,θ) of P as follows: r = i + j = √2 e_r