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Study Guide -- Momentum, Center of Mass (Mr. Rogers AP Physics C ) |
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Momentum |
Impulse |
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P = mv |
Imp = DP |
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Imp = Ft
for constant force |
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Imp
= ∫ F(t)
∙ dt |
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Note: the area under the F vs. time curve equals the change in
an object's momentum. |
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Newton's 2nd Law |
Center of Mass |
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S F = dP / dt |
| xcm = (S mixi
) / (S mi ) |
xcm =1/m
∫ x dm |
| ycm = (S miyi
) / (S mi ) |
ycm = 1/m
∫ y dm |
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Rockets |
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Thrust = vm dm/dt |
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Elastic Collision:
- momentum is conserved
- kinetic energy is conserved.
- The particles do not stick
together
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Momentum is a vector:
All the rules for vectors apply. For example, when add 2 momentum
vectors in different dimensions, you cannot simply sum their
magnitudes. You must use vector addition:
P = (Px2 + Py2)
0.5
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Inelastic Collision:
- momentum is conserved
- kinetic energy is not
conserved.
- The particles stick together
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Explosion of moving objects: If
a moving object explodes, the center of mass will continue along the
same path as it would have even without the explosion. |
| Rockets: Rockets behave similar
to exploding devices. In outer space the rocket's center of mass
(including its fuel) will remain in the same location. Rocket
thrusters must expel mass to move forward. |
Impulse and Newton's 3rd Law:
When two objects collide the impulse on one is equal in magnitude but
opposite in direction to the impulse on the other. Impulse is a vector
and Newton's 3rd law applies to it just like it applies to forces. |
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Problem Solving Tips: Momentum |
| Multi-dimensional momentum problems:
Think components! |
| Center of Mass (CM): When
calculating the CM, the location of the origin is arbitrary. Always
place it in a convenient place that simplifies the problem. Note that
the center of mass is like a balance point. If you imagine placing a
fulcrum under the CM, the object should look like it is balanced on
it. |
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| Ballistic Pendulum: The ballistic
pendulum uses a combination of conservation of energy and conservation
of momentum to find the velocity of a projectile. |
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| Momentum |
Elastic collision |
Center of Mass |
| Impulse |
Inelastic collision |
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