1. Engineering Mechanics : DYNAMIC
DAJ ( STATICS & DYNAMICS )
Lecture #13
By,
Noraniah Kassim
Hairul Mubarak b Hassim
Universiti Tun Hussein Onn Malaysia (UTHM),
DAJ ( Statics & Dynamics)

2. DAJ 21003 ( Statics & Dynamics)
Objective
• To investigate particle motion along a curved path “Curvilinear Motion” using three coordinate systems
Rectangular Components
• Position vector r = x i + y j + z k
• Velocity v = vx i + vy j + vz k (tangent to path)
• Acceleration a = ax i + ay j +az k (tangent to hodograph)
– Normal and Tangential Components
– Polar & Cylindrical Components
DAJ ( Statics & Dynamics)

3. Normal and Tangential Components
If the path is known i.e. – Circular track with given radius – Given function • Method of choice is normal and tangential components
DAJ ( Statics & Dynamics)

4. DAJ 21003 ( Statics & Dynamics)
Position
From the given geometry and/or given function
More emphasis on radius of curvature velocity and acceleration
DAJ ( Statics & Dynamics)

5. DAJ 21003 ( Statics & Dynamics)
Planer Motion
At any instant the origin is located at the particle it self
The t axis is tangent to the curve at P and + in the direction of increasing s.
The normal axis is perpendicular to t and directed toward the center of curvature O’.
un s the unit vector in normal direction
ut is a unit vector in tangent direction
DAJ ( Statics & Dynamics)

6. Radius of curvature (r)
For the Circular motion :(r) = radius of the circle
For y = f(x):
DAJ ( Statics & Dynamics)

7. DAJ 21003 ( Statics & Dynamics)
Example
Find the radius of curvature of the parabolic path in the figure at x = 150 m.
DAJ ( Statics & Dynamics)

8. DAJ 21003 ( Statics & Dynamics)
Velocity
The particle velocity is always tangent to the path.
Magnitude of velocity is the time derivative of path function s = s(t)
- From constant tangential acceleration
– From time function of tangential acceleration
– From acceleration as function of distance
DAJ ( Statics & Dynamics)

9. DAJ 21003 ( Statics & Dynamics)
Acceleration
Acceleration is time derivative of velocity
DAJ ( Statics & Dynamics)

10. DAJ 21003 ( Statics & Dynamics)
Special case
1)Straight line motion
2)Constant speed curve motion (centripetal acceleration)
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11. Centripetal acceleration
Recall that acceleration is defined as a change in velocity with respect to time.
Since velocity is a vector quantity, a change in the velocity’s direction , even though the speed is constant, represents an acceleration.
This type of acceleration is known as
Centripetal acceleration
DAJ ( Statics & Dynamics)

12. DAJ 21003 ( Statics & Dynamics)
Acceleration
3 types of acceleration: linear,radial (centripetal) & angular
Linear acceleration: is a change in speed without change in direction (increase in thrust in straight-and-level flight)
Radial (or centripetal) acceleration : when there is a change in direction (turn, dive)
Angular acceleration: when body speed and direction are changed (tight spin)
DAJ ( Statics & Dynamics)

13. DAJ 21003 ( Statics & Dynamics)
Example 1
The jet plane travels along the vertical parabolic path. When it is at point A it has a speed of 200m/s, which is increasing at the rate 0.8m/s2. Determine the magnitude of acceleration of the plane when it is at point A.
DAJ ( Statics & Dynamics)

14. DAJ 21003 ( Statics & Dynamics)
Example 2
At a given instant the jet plane has a speed of 200 m/s and an acceleration of 35m/s^2 acting in the direction shown. Determine the rate of increase in the plane’s speed and the radius of curvature ρ of the path.
DAJ ( Statics & Dynamics)

15. DAJ 21003 ( Statics & Dynamics)
Example 3
A car is traveling along a circular curve that has a radius of 50m. If its speed is 16m/s and is increasing uniformly at 8m/s^2, determine the magnitude of its acceleration at this instant.
DAJ ( Statics & Dynamics)

16. Three-Dimensional Motion
For spatial motion required three dimension.
Binomial axis b which is perpendicular to ut and un is used
ub= ut x un
DAJ ( Statics & Dynamics)