Physics 2211 Mechanics Review 3 Chapters 1013

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Physics 2211 - MechanicsReview 3Chapters
10-13

• Dr. John Evans

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Vector Cross Product
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Example Cross Product with Cartesian Unit Vectors
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Vector Torque andAngular Momentum
We can also define the torque t and the angular
momentum L as vectors
This is the rotational equivalent of
Newtons 2nd Law Fnet dp/dt ( ma)
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The Angular Momentumof a Rigid Body
The angular momentum L of an isolated system
(tnet0) is conserved. The final angular
momentum Lf is equal to the initial angular
momentum Li.
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Angular Momentumand Angular Velocity
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Example The Angular Momentum of the Earth
What is the angular momentum of the Earth as
it spins on its axis?
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ExampleTwo Interacting Disks
A 20 cm diameter 2.0 kg solid disk is
rotation at 200 rpm. A stationary 1.0 kg 20 cm
diameter circular loop is dropped straight down
onto the rotating disk. Friction causes the loop
to accelerate until it is riding on the disk.
What is the angular velocity of the combined
system?
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Chapter Summaries

• Chapters 10 - 13

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Chapter 10 Summary (1)
Conservation of energy E1f E2f E1i
E2iTherefore, E1f - E1i -(E2f - E2i) or
DE1 -DE2
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Chapter 10 Summary (2)
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Chapter 10 Summary (3)
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Review of Conservation Laws (1)
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Review of Conservation Laws (2)
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Example Dragging a Block (1)
A spring is attached to a 2 kg block. The
other end is pulled by a motorized toy train that
moves forward at 5.0 cm/s. The spring constant is
k50 N/m and the coefficient of static friction
between the block and the surface is ms0.6. The
spring is in equilibrium at t0 s when the train
starts to move. At what time does the block
start to slip?
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Example Dragging a Block (2)
This is an example of stick-slip motion, which
is common in nature. Example behavior of rocks
during seismic activity and earthquakes.
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Chapter 11 Summary (1)
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Chapter 11 Summary (2)
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Chapter 11 Summary (3)
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ExampleUsing Work to Find Car Speed
A 1500 kg car accelerates from rest with a
net force that decreases linearly with position
from 10,000 N to zero, as shown. What is
the cars speed after traveling 200 m?
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ExampleThe Power Output of a Motor
A factory uses a motor and cable to drag a
300 kg machine into the proper place on the
factory floor. (mk0.60.) What power must
be supplied to drag the machine across the floor
at a speed of 0.50 m/s?
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Chapter 12 Summary (1)
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Chapter 12 Summary (2)
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Chapter 12 Summary (3)
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Example Escape Speed
A 1000 kg rocket is fired straight away from
the surface of the Earth. What speed does it
need to escape from the gravitational pull of
the Earth and never return? (Assume a
non-rotating Earth.)
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ExampleRaising a Satellite - LEO to Geo
How much work must be done in boosting a
1000 kg communication satellite from low Earth
orbit (h300 km) to geosynchronous orbit?
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Chapter 13 Summary (1)
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Chapter 13 Summary (2)
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Chapter 13 Summary (3)
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Example Rotating Rockets
Far out in space, a 100,000 kg rocket and a
200,000 kg rocket are docked at opposite ends of
a motionless 90 m long connecting tunnel. The
tunnel is rigid and its mass is much less than
that of either rocket. The rockets start their
engines simultaneously and fire in opposite
directions, each generating 50,000 N of thrust.
What is the angular velocity w of the structure
after 30 s?
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End of Review 3