Solved Example & Practice Problems: Radial and Transverse Components (Polar Co-ordinates)

Radial and Transverse Components (Polar Co-ordinates) - Dynamics of Particles

Solved Examples for Understanding

Example 9.9.1 

Link OB rotates about hinge O in vertical plane in anticlockwise direction starting from horizontal position. A collar can slide on the link as shown in Fig. 9.9.2. Angular position of link is given by θ = 0.5t2 and position of collar from hinge is given by r = 2t - 0.3t2, with the terms having usual meaning and S.I. units. Compute magnitude of velocity and acceleration of collar when θ = 60°.

Solution: 

Example 9.9.2 

The slotted arm AB drives the pin through the spiral groove described by the equation r=0.2eθ where r is in meters and θ in radians. If θ = 3 rad/s and is constant, determine the transverse compoment of the pin's acceleration when θ = 120°. Refer Fig. 9.9.3.

Solution :

Example 9.9.3 

A circle of radius 'b' rolls over other fixed circle at some radius without slipping. A point on the circumference of rolling circle describes a cardioid defined by equations Obtain radial and transverse components of velocity and acceleration of the point when t = 1 s.

Solution:

Examples for Practice

Q.1

A partial 'P' moves along the spiral path where θ is in radians. If it maintains a constant speed of v = 6 m/s, determine the magnitude of vr and vθ as a function of θ and evaluate each at θ = 1 radian. Refer Fig. 9.9.4.

Q.2

The car travels around the circular track such that its transverse component is θ = (0.006 t2) rad, where t is in seconds. Determine the radial and transverse components of velocity and acceleration of the car at the instant t = 4 s. Refer Fig. 9.9.5.