Kinetic Equilibrium Reconstruction and Stability Analysis ...
Torque,stability and equilibrium
-
Upload
elaine-espiel -
Category
Education
-
view
136 -
download
0
Transcript of Torque,stability and equilibrium
![Page 1: Torque,stability and equilibrium](https://reader036.fdocuments.net/reader036/viewer/2022062306/58ed95b21a28ab97178b47d1/html5/thumbnails/1.jpg)
*door top view F1F2
axis of rotation r1
r2
Where:F = forcer = lever arm= perpendicular distance from the axis of rotation to the line along which the forces acts.here.,α∝ F
![Page 2: Torque,stability and equilibrium](https://reader036.fdocuments.net/reader036/viewer/2022062306/58ed95b21a28ab97178b47d1/html5/thumbnails/2.jpg)
*door top view F1F2
axis of rotation r1
r2
α ∝ F x r Moment of Force or Torque (τ)
α ∝ τ
![Page 3: Torque,stability and equilibrium](https://reader036.fdocuments.net/reader036/viewer/2022062306/58ed95b21a28ab97178b47d1/html5/thumbnails/3.jpg)
a vector quantity that determines the ability of a force to introduce rotation. τ = rF ; unit: mN
1.Magnitude of the applied force2.Distance from point of application to
pivot (location of applied force)3.Angle ( direction of the applied force)
![Page 4: Torque,stability and equilibrium](https://reader036.fdocuments.net/reader036/viewer/2022062306/58ed95b21a28ab97178b47d1/html5/thumbnails/4.jpg)
F1
F2
F3
r1
r2
τ F1 > τ F2
τ F2 < τ F1
τ = 0
NOTE: in general τ = r⊥F
Remind us that we must use the distance from
the axis of rotation that is perpendicular to the
line of action of the force
r⊥ = r sin ⴱ
![Page 5: Torque,stability and equilibrium](https://reader036.fdocuments.net/reader036/viewer/2022062306/58ed95b21a28ab97178b47d1/html5/thumbnails/5.jpg)
F2
ⴱτ = rF⊥l = rF⊥ sinⴱ
We can use τ = r⊥ F or τ = r F⊥ or τ = r F sin ⴱ to calculate the torque whichever is easiest.Line of action of a force - the line of motion of a force is an imaginary line of indefinite length drawn a long the direction of the forceThe moment arm is the perpendicular distance from the line of action of a force to the axis of rotation.
![Page 6: Torque,stability and equilibrium](https://reader036.fdocuments.net/reader036/viewer/2022062306/58ed95b21a28ab97178b47d1/html5/thumbnails/6.jpg)
1. An 80 N acts at the end of a 12 cm wrench as shown. Find the torque.
80 N12 cm ⴱ =60o
2. Find the resultant torque about axis A for the arrangement shown:
ⴱ =30o ⴱ =30o 4 m
2 m6 m
F3 = 20 N
F2 = 40N
F1 = 30 N
![Page 7: Torque,stability and equilibrium](https://reader036.fdocuments.net/reader036/viewer/2022062306/58ed95b21a28ab97178b47d1/html5/thumbnails/7.jpg)
Torque is a vector quantity that has a direction as well as magnitude
Thumb F (force)Pointer r (moment arm)Middle finger direction of τ (torque)
![Page 8: Torque,stability and equilibrium](https://reader036.fdocuments.net/reader036/viewer/2022062306/58ed95b21a28ab97178b47d1/html5/thumbnails/8.jpg)
![Page 9: Torque,stability and equilibrium](https://reader036.fdocuments.net/reader036/viewer/2022062306/58ed95b21a28ab97178b47d1/html5/thumbnails/9.jpg)
↑ Up +↓ Down -
→ Right +← left -⊙ Outward +⊗ Inward -CC Counterclockwise +C clockwise -
![Page 10: Torque,stability and equilibrium](https://reader036.fdocuments.net/reader036/viewer/2022062306/58ed95b21a28ab97178b47d1/html5/thumbnails/10.jpg)
→ ⊗ ↑
← ⊙⊙ →
↑
↑
![Page 11: Torque,stability and equilibrium](https://reader036.fdocuments.net/reader036/viewer/2022062306/58ed95b21a28ab97178b47d1/html5/thumbnails/11.jpg)
Car at rest Constant speed, no change in direction
An object is said to be in equilibrium if it does not have linear acceleration and angular acceleration
Linear acceleration is Zero if….
![Page 12: Torque,stability and equilibrium](https://reader036.fdocuments.net/reader036/viewer/2022062306/58ed95b21a28ab97178b47d1/html5/thumbnails/12.jpg)
Angular acceleration is Zero if….
wheel at rest Constant rotation
![Page 13: Torque,stability and equilibrium](https://reader036.fdocuments.net/reader036/viewer/2022062306/58ed95b21a28ab97178b47d1/html5/thumbnails/13.jpg)
![Page 14: Torque,stability and equilibrium](https://reader036.fdocuments.net/reader036/viewer/2022062306/58ed95b21a28ab97178b47d1/html5/thumbnails/14.jpg)
![Page 15: Torque,stability and equilibrium](https://reader036.fdocuments.net/reader036/viewer/2022062306/58ed95b21a28ab97178b47d1/html5/thumbnails/15.jpg)
The center of mass lies at the geometric center for a
symmetric, uniform density object.
h/3
hR
h/2
h
h/2
h
![Page 16: Torque,stability and equilibrium](https://reader036.fdocuments.net/reader036/viewer/2022062306/58ed95b21a28ab97178b47d1/html5/thumbnails/16.jpg)
The center of mass can be outside the mass of the body.
Center of mass
![Page 17: Torque,stability and equilibrium](https://reader036.fdocuments.net/reader036/viewer/2022062306/58ed95b21a28ab97178b47d1/html5/thumbnails/17.jpg)
Ability of an object to return to its original position after it is displaced or tilted slightly
- CG is below of point of support- the objects return to its original position
- When object is displaced, the object moves even farther from its position
- When object is displaced, the object remain in its position
![Page 18: Torque,stability and equilibrium](https://reader036.fdocuments.net/reader036/viewer/2022062306/58ed95b21a28ab97178b47d1/html5/thumbnails/18.jpg)
![Page 19: Torque,stability and equilibrium](https://reader036.fdocuments.net/reader036/viewer/2022062306/58ed95b21a28ab97178b47d1/html5/thumbnails/19.jpg)
![Page 20: Torque,stability and equilibrium](https://reader036.fdocuments.net/reader036/viewer/2022062306/58ed95b21a28ab97178b47d1/html5/thumbnails/20.jpg)
![Page 21: Torque,stability and equilibrium](https://reader036.fdocuments.net/reader036/viewer/2022062306/58ed95b21a28ab97178b47d1/html5/thumbnails/21.jpg)
cm
![Page 22: Torque,stability and equilibrium](https://reader036.fdocuments.net/reader036/viewer/2022062306/58ed95b21a28ab97178b47d1/html5/thumbnails/22.jpg)