More motion topics
Momentum
momentum is equal to the product of an object’s
mass and its velocity.
p=mv
150 kg offensive lineman runs 5 m/s
p = (150 kg)(5 m/s) = 750 kg m/s
90 kg running back runs 9 m/s
p = (90 kg)(9 m/s) = 810 kg m/s
The running back has more momentum.
Momentum
Momentum is a conserved quantity
• why the newton’s cradle works (swinging balls)
• useful for studying collisions
– The total momentum before the crash is equal to the
total momentum after the crash.
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see examples:
http://en.wikipedia.org/wiki/Elastic_collision
http://www.fearofphysics.com/Collide/collide.html
http://www.glenbrook.k12.il.us/gbssci/Phys/mmedi
a/momentum/cbb.html
Momentum
When two cars crash and stick together the
momentum is conserved. The two cars will
move together with the same final velocity.
m1v1 + m2v2 = (m1 + m2)vf
Two cars of the same weight crash into each
other. One of the cars was initially sitting still.
mv0 + m(0) = (m+m)vf
v f = ½ v0
The cars move together with half the velocity
of the first car.
Momentum
We can use the equation on the previous slide to
determine how fast a gun shoots.
By firing a bullet into a block and knowing the
masses and the speed the block obtains after
being shot, we can calculate how fast the bullet
was shot.
This is easy to do as long as the block is a lot
more massive than the bullet.
Momentum – shooting a gun
When you shoot a gun, the gun recoils. This is
because of conservation of momentum.
Initially the momentum is zero.
The bullet gets momentum in one direction.
The gun get momentum in the opposite
direction.
Momentum is a vector, so one of the
momentums will be in the negative direction.
The two final momentums add up to zero.
Momentum - rocket
Works the same as shooting a gun, except you
are continuously firing ‘bullets’ (expelling gas).
Gas gets momentum in one direction.
The rocket gets momentum in the opposite
direction.
Momentum - explosions
An explosion can be treated as a collision in
reverse.
First an object has a momentum.
After the explosion, all the momentums of the
individual fragments add up to the original
momentum.
Momentum
• Collision in two dimensions
• In two or three dimensions, the same rule applies.
• Now you have to the fact that momentum is
conserved in each direction.
• http://www.youtube.com/watch?v=KteP6k1wg94
Momentum
If you want to change the momentum of an
object, an outside force is required.
F = p/ t
F t= p
F t is called an impulse.
Impulse equals the change in momentum
Rotational Momentum
• Rotational or angular momentum is the
equivalent to momentum when we study
rotating objects.
Rotational inertia – an objects tendency to resist
changes in how fast it spins. This is the rotational
analogy to mass. This is determined by how far
the mass is from the rotation point.
angular velocity – the rate that an object spins.
Angular momentum
• Earlier we saw p = m v
• now for angular momentum: L = I
• to change the angular momentum, a torque must be
applied. Torque comes from a force applied off center
from the rotation axis.
• With no outside torques, angular momentum is a
conserved quantity.
– if rotational inertia is reduced, the object spins faster
• example is an ice skater
• rotating star
Rolling motion
• Earlier we rolled some objects down a ramp.
• Round objects with different mass distributions
(disk, ball, hoop) rolled down with different
speeds.
• They have different rotational inertias. As they
start rolling, different amounts of energy is
needed for rotation that is taken away from
translation.
Rolling motion
Race a hoop against a disk. (each of radius r)
All of the hoop’s mass is r away from the center.
Some of the disk’s mass is closer than r from center.
The hoop has more rotational inertia.
Harder for the hoop to start rolling.
Angular velocity of the hoop speeds up slower.