King Fahd University of Petroleum & Minerals Mechanical Engineering Dynamics ME 201 BY Dr. Meyassar N. Al-Haddad Lecture # 8

Relative Motion (Translating Axes) - Consider two particles A and B. Both are moving with respect to fixed axes X-Y - The translating axes x-y is moving with particle B - The position vector of the particle A measured relative to the x-y axes is (A/B means A with respect to B) Relative-Motion Analysis of Two Particles Using Translating Axes

KINEMATICS OF PARTICLES If is the absolute position of B, then Take derivative with respect to time : or and

AB 160 km/h180 km/h

EXAMPLE The passenger aircraft B is flying east with velocity v B = 800 km/h. A jet is traveling south with velocity v A = 1200 km/h. What velocity does A appear to a passenger in B ? Solution x y

EXAMPLE (Cont.) Absolute value : The direction of x y West of South

Example 

At the instant shown, the car at A is traveling at 10 m/s around the curve while increasing its speed at 2 m/s 2. The car at B is traveling at 18.5 m/s along the straightway and increasing its speed at 5 m/s 2. Determine the relative velocity and relative acceleration of A with respect to B at this instant Problem