Rigid_body (11111111111111111111111111111111111111).pdf

rigid

1. ROTATION OF A RIGID OBJECT
1
BY PACHARA JOLUTSAKUL
ПАШАРА Я ХОРОШО ЖУК

2. CONTENT
- Introduction
- Angular displacement, velocity, acceleration
- Rotational and translational motion
- Torque
- Moment of inertia
- Rolling motion
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3. INTRODUCTION
- The motion around a fixed axis, but linear motion is
along a straight path
- A rigid object maintains its shape during motion, but a
particle has no size or shape
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4. ANGULAR DISPLACEMENT
OLN?
?L
O
N
??L?
?F?
?
- The rate of change of angular position with respect to time
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5. ANGULAR VELOCITY
?
???L
??
?P
?L
@?
@P
- The rate of change of angular displacement with respect to time
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6. ANGULAR ACCELERATION
?
???L
??
?P
?L
@?
@P
- The rate of change of angular velocity with respect to time
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7. WE ALL ARE VECTOR!
- Right - hand rule
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8. ROTATIONAL AND TRANSLATIONAL MOTION (1)
- Just change..
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9. EXAMPLE 1 (1)
A wheel rotates with a constant angular acceleration of 3.50 rad/s
2
.
a) If the angular speed of the wheel is 2.00 rad/s at t = 0, through what angular
displacement does the wheel rotate in 2.00 s?
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10. EXAMPLE 1 (2)
b) Through how many revolutions has the wheel turned during this time
interval?
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11. EXAMPLE 1 (3)
c) What is the angular speed of the wheel at t = 2.00 s?
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12. LINEAR VELOCITY
RL
@O
@P
L
N@?
@P
LN?
=L
@R
@P
L
N@?
@P
LN?
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13. TORQUE
- Thing that try to rotate a rigid object
?LN(OEJ?L(@
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14. SUMMATION OF TORQUE
- Torque is a vector
??L?
5E?
6L(@
5F(@
6
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15. MOMENT OF INERTIA
- A measure of an object’s resistance to changes in its rotation
??L+??(LI=
MOMENT OF INERTIAMASS
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16. CALCULATE MOMENT OF INERTIA
- A rigid body is divided into many small pieces
+L?N
6
@IL??N@8
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17. EXAMPLE 2
Calculate the moment of inertia of a uniform thin rod of length L and mass M
about an axis perpendicular to the rod (the y’ axis) and passing through its
center of mass.
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18. EXAMPLE 3
A uniform solid cylinder has a radius R, mass M, and length L. Calculate its
moment of inertia about its central axis (the z axis).
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19. PARALLEL-AXIS THEOREM
- To find moment of inertia when change a rotation axis
+L+
??E/&
6
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20. EXAMPLE 4
Find the moment of inertia of the rod of mass M and length L about an axis
perpendicular to the rod through one end (the y axis).
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21. MOMENT OF INERTIA OF SOME RIGID OBJECTS (1)
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22. MOMENT OF INERTIA OF SOME RIGID OBJECTS (2)
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23. ROTATIONAL AND TRANSLATIONAL MOTION (2)
- Just change..
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24. EXAMPLE 5 (1)
Two blocks having different masses m
1 and m
2 are connected by a string
passing over a pulley. The pulley has a radius R and moment of inertia I about
its axis of rotation. The string does not slip on the pulley, and the system is
released from rest. Find the translational speeds of the blocks after block 2
descends through a distance h and find the angular speed of the pulley at this
time.
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25. EXAMPLE 5 (2)
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26. ROLLING MOTION
- Pure rolling motion is rolling without slipping
R
??L4?
=
??L4?
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27. PURE ROLLING MOTION
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28. REFERENCE
28
- Serway, R.A. and Jewett, J.W. (2014) Physics for Scientists
and Engineers with Modern Physics. 9th Edition.

29. REFERENCE
28
- Serway, R.A. and Jewett, J.W. (2014) Physics for Scientists
and Engineers with Modern Physics. 9th Edition.

30. REFERENCE
28
- Serway, R.A. and Jewett, J.W. (2014) Physics for Scientists
and Engineers with Modern Physics. 9th Edition.

31. REFERENCE
28
- Serway, R.A. and Jewett, J.W. (2014) Physics for Scientists
and Engineers with Modern Physics. 9th Edition.

32. REFERENCE
28
- Serway, R.A. and Jewett, J.W. (2014) Physics for Scientists
and Engineers with Modern Physics. 9th Edition.