Term
| Total moment of all the forces about the centre of mass |
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Definition
[image]
For a lamina, the sum is equal to the mass moment of inertia about the centre of gravity times the angular acceleration. |
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Term
| D'Alembert Forces and Moments |
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Definition
Just like with the forces, the d'alembert moments directly oppose the accelerations, but this time it is the angular acceleration.
[image]
When taking into account both the d'alembert's forces and moments [image] should always be included as a moment, regardless of the point the moment is being taken from.
[image] |
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Term
| Momentum equations and their integrals |
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Definition
[image]
The rate of change of angular momentum of any point is equal to the total moment about the point.
Furthermore, from this another equation can be inferred:
[image] |
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Term
| What happens when external torque applied to a system about a given point is zero? |
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Definition
Angular momentum is conserved.
[image] |
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Term
| Total kinetic energy of a rigid body that can translate and rotate |
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Definition
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Term
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Definition
[image]
Where F is the total external force. Therefore, impulse is the net change in linear momentum.
Also, the moment of the impulse about a fixed point O or the moving centre of gravity G is equal to the corresponding change in angular momentum. |
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Term
| Method for impulse questions |
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Definition
1. Draw three diagrams for 'before', 'during' and 'after' the impact. Each diagram should be in the same configuration (at the moment of impact). 'Before' and 'After' should define respective velocities and the 'during' diagram should be a FBD only showing impulses (ignoring non-impulsive forces, because by definition impulses are infinite and as such other forces are negligible).
2. Equate linear momentum change to impulsive forces (as vectors for each component).
3. Equate angular momentum change to impulsive moments (planar motion so only one component). |
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Term
| Rules to follow when completing a question |
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Definition
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