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					A net torque is analogous to a net force when
      examining its influence on motion.

                        Newton's First Law (adapted to
                        torque)
                             In the absence of a net torque, an
                             object will continue with its
                             present rotational (angular)
                             velocity.
                        Newton's Second Law (adapted to
                        torque)
                             If there is a net torque, the object
                             will have a rotational (angular)
                             acceleration according to
                             t=I*a.
                        Newton's Third Law (remains
                        unchanged for torque)
                             When one object applies a force
                             on another object the second
                             object applies an equal and
                             opposite force back on the first
                             object.
Equations of Motion for Constant Linear Acceleration
       and for Constant Angular Acceleration
   Suppose you are a visitor on
 another planet and observe the
setting sun. You notice that your
little finger, which is 1 cm wide,
  just covers the sun when you
  extend your arm out and hold
your finger 1 m away from your
eyes. The bottom edge of the sun
begins to dip below the horizon,
    and 5 minutes later the sun
completely disappears. Estimate
   the length of the day on this
               planet.
      The Crab nebula resulted from a
supernova explosion seen in the year 1054.
In addition to the gaseous debris seen here,
 the explosion left a spinning neutron star
   (pulsar) at its center. This pulsar has a
  period of rotation of T = 0.033 s that is
   increasing at the rate of 1.26x10 -5 s/y.
Assuming a constant angular acceleration,
   in how many years from now will the
pulsar stop rotating? What was the initial T
                for the pulsar?
      This massive shield door at a neutron test facility at Lawrence Livermore
Laboratory is the world's heaviest hinged door. The door has a mass of 44,000 kg,
 a rotational inertia about a vertical axis through its huge hinges of 8.7x10 4 kg·m2,
and a (front) face width of 2.4 m. Neglecting friction, what steady force, applied at
  its outer edge and perpendicular to the plane of the door, can move it from rest
                           through an angle of 90° in 30 s?
 A block with mass m = 1.2 kg hangs from a massless cord that is wrapped
 around the rim of a uniform disk of mass M = 2.5 kg and radius R = 20 cm,
mounted on a fixed horizontal axle. Assuming the cord does not slip and there
  is no friction at the axle, find the acceleration of the falling block and the
                                tension in the cord.




                                                  Fnet,y = may

                                                   tnet = Ia

                                                   at = ar
A uniform ball, of mass M = 6.00 kg and radius R, rolls smoothly from rest
down a ramp at angle q = 30.0°. What is its speed at the bottom, a vertical
 distance h = 1.20 m below? What are the magnitude and direction of the
            friction force on the ball as it rolls down the ramp?
If the turntable’s moment of inertia is 5 times that of the record, what is
 the rotational speed of the record-turntable system after the collision?
 For a classroom demonstration, Cameron sits on a piano stool holding a
      sizable mass in each hand. Initially, the student holds his arms
outstretched and spins about the axis of the stool with an angular speed of
 3.74 rad/s. The moment of inertia in this case is 5.33 kg*m 2. While still
 spinning, the student pulls his arms in to his chest reducing the moment
     of inertia to 1.6 kg*m2. What is Cameron’s angular speed now?
The spinning ice-skater
Why does the cat always
   land on its feet?
Frontside 180
More examples…
The wheel shown has 8 equally spaced spokes and a radius of 30 cm. It is
mounted on a fixed axle and is spinning at 2.5 rev/s. You want to shoot a
  20-cm-long arrow parallel to this axle and through the wheel without
hitting any of the spokes. Assume that the arrow and the spokes are very
 thin. (a) What minimum speed must the arrow have? (b) Does it matter
 where between the axle and rim of the wheel you aim? If so, what is the
                              best location?
What’s the acceleration of the falling hand?
Will the ball land into the cup?
                                                                                In early 1985, Test Devices, Inc.
                                                                           (www.testdevices.com) was spin-testing a
                                                                             sample of a solid steel rotor (a disk) of
                                                                           mass M = 272 kg and radius R = 38.0 cm.
                                                                              When the sample reached an angular
                                                                               speed w of 14000 rev/min, the test
                                                                           engineers heard a dull thump from the test
                                                                           system, which was located one floor down
                                                                            and one room over from them. Just how
                                                                           much energy was released in the explosion
                                                                                           of the rotor?

Damage caused by the explosion included:
•lead bricks thrown out in the hallway leading to the test room
•a door to the room had been hurled into the adjacent parking lot
•one lead brick shot from the test site through the wall of a neighbor's
kitchen
•the structural beams of the test building had been damaged
•the concrete floor beneath the spin chamber had been shoved
downward by about 0.5 cm
•the 900-kg lid blown upward through the ceiling and then crashed
back onto the test equipment
   An early method of measuring the
 speed of light makes use of a rotating
 slotted wheel. A beam of light passes
through a slot at the outside edge of the
 wheel, travels to a distant mirror, and
returns to the wheel just in time to pass
  through the next slot in the wheel. In
 one such setup, the wheel has a radius
of 5.0 cm, has 500 slots at its edge, and
the mirror is L = 500 m from the wheel.
 If the wheel turns at a rate of 3.8x103
rad/s and the light beam passes through
    two neighboring slots, what is the
        measured speed of light?
                                                                                  In early 1985, Test Devices, Inc.
                                                                            (www.testdevices.com) was spin-testing a
                                                                           sample of a solid steel rotor (a disk) of mass
                                                                            M = 272 kg and radius R = 38.0 cm. When
                                                                             the sample reached an angular speed w of
                                                                             14000 rev/min, the test engineers heard a
                                                                           dull thump from the test system, which was
                                                                            located one floor down and one room over
                                                                            from them. Evidently quite a bit structural
                                                                            damage had been caused by the explosion.
                                                                               How much energy was released in the
                                                                                       explosion of the rotor?


Damage caused by the explosion included:
•lead bricks thrown out in the hallway leading to the test room
•a door to the room had been hurled into the adjacent parking lot
•one lead brick shot from the test site through the wall of a neighbor's
kitchen
•the structural beams of the test building had been damaged
•the concrete floor beneath the spin chamber had been shoved
downward by about 0.5 cm
•the 900-kg lid blown upward through the ceiling and then crashed
back onto the test equipment

				
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