1. Kinetics (I) Review of Kinetics of Planar Mechanisms5
Kinetics (I)
Review of Kinetics of Planar Mechanisms
- Inertia (mass and moment of inertia)
- Governing equation (Newton’s Law)
2. Moment/Product of Inertia – spatial rotation
ME 316 Lecture 6

2. Kinetics: how does a body move under the force or moment ?
Review of Planar Kinetics of a Rigid Body
Kinetics: how does a body move under the force or moment ?
If there is no any force applied to a body then the body will
remain its current status
Motion or no-motion in a specific direction
Total resultant force in a direction
The above is called “Newton First Law”
ME 316 Lecture 6

3. Review of Planar Kinetics of a Rigid Body
The basic evidence to support the Newton First Law is the inertia
A property of an object;
A measure of how difficult or easy the motion of a body can be changed;
3. An inherent resistance to change
ME 316 Lecture 6

4. IA ≠ IB Review of Planar Kinetics of a Rigid Body
Two types of inertia depending on types of causes
Cause is force: inertia is mass (m)
Cause is moment: inertia is the moment of inertia (IP) A
IA ≠ IB B
ME 316 Lecture 6

5. IA ≠ IB Review of Planar Kinetics of a Rigid Body
Example (to be filled)
IA ≠ IB
ME 316 Lecture 6

6. Review of Planar Kinetics of a Rigid Body
Parallel – axis theorem
(to be filled) B G
G is the center of gravity
ME 316 Lecture 6

7. Review of Planar Kinetics of a Rigid Body
Kinetic energy (K)
Translation (T) (to be filled)
Rotation (R) (to be filled)
General (T + R) (to be filled)
ME 316 Lecture 6

8. Review of Planar Kinetics of a Rigid Body
Kinetics Equation
Translation:
X and Y axes may not be horizontal or vertical; rather they could be in any direction but not in parallel.
ME 316 Lecture 6

9. Review of Planar Kinetics of a Rigid Body
Rotation:
Case 1: G P
May not be
fixed
ME 316 Lecture 6

10. Review of Planar Kinetics of a Rigid Body
Case 2:
P=G (mass center)
ME 316 Lecture 6

11. Review of Planar Kinetics of a Rigid Body
Case 3: when P is fixed point
ME 316 Lecture 6

12. Review of Planar Kinetics of a Rigid Body
Translation and rotation or or
ME 316 Lecture 6

13. Moment/product of Inertia of Spatial Rotationz
ME 316 Lecture 6

14. Product of Inertia
Orthogonal planes
ME 316 Lecture 6

15. Product of Inertia x
ME 316 Lecture 6

16. Product of Inertia
If either one or both of the orthogonal planes are planes of symmetry for the mass, the product of inertia with respect to these planes will be zero.
ME 316 Lecture 6

17. Moment /Product of Inertia
Parallel-axis and parallel-plane theorems
ME 316 Lecture 6

18. Moment /Product of Inertia
Inertia Tensor – a compact way to express
ME 316 Lecture 6

19. Moment /Product of Inertia
Principal axes - principal moments of inertia
If the coordinate axes are oriented such that two of the three orthogonal planes containing the axes are planes of symmetry for the body, then all the products of inertia for the body are zero with respect to the coordinate planes, and hence the coordinate axes are principal axes of inertia
ME 316 Lecture 6

20. Moment /Product of Inertia
Moment of inertia about an arbitrary axis
ME 316 Lecture 6

21. Moment /Product of Inertia The bent rod ABCD has a weight of 1.5 lb/ft
Example 1
Find: the location of center of gravity G and Ix’, Iy’, Iz’
ME 316 Lecture 6

22. Moment /Product of Inertia
The 1.5 Kg rod and 4 Kg disk
Example 2
Find: Iz’ of the composite body
ME 316 Lecture 6

23. Moment /Product of Inertia
The bent rod OABC has mass of 4 Kg/m
Example 3
Find: Ix’x’ of the rod
ME 316 Lecture 6