1. King Fahd University of Petroleum & Minerals
Mechanical Engineering
Dynamics ME 201 BY
Dr. Meyassar N. Al-Haddad
Lecture # 7

2. From one particle to two particles

3. 12.9 Absolute Dependent Motion Analysis of Two Particles
The motion of one particle will depend on the corresponding motion of another part
Inextensible cords connection

4. Position How to establish the position coordinate
Reference from a fixed point (O) or fixed datum.
Measures along each inclined plane in the direction of motion
Has positive sense from C to A and D to B.
Establish a total cord length equation

5. Velocity Velocity is the time derivative of the position
From the total cord length equation
Velocity

6. Acceleration Acceleration is the time derivative of the velocity
From the velocity equation
Acceleration

7. Example
Position coordinate
Velocity
Acceleration

8. Example
Position coordinate
Velocity
Acceleration
Positive signs, why?

9. Example 12.21 Position coordinate “cord equation” Velocity
Acceleration

10. Example 12.22 Position coordinate “cord equation” Velocity
Acceleration

11. Example 12.22
Establish a relation y = f(x)

12. Relative-Motion Analysis of Two Particles Using Translating Axes
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)

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

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

16. EXAMPLE (Cont.) ANS ANS Absolute value : The direction ofy
West of South x
ANS

17. Thank you