Physics 197 Lecture Notes - Lecture 20: Point Particle, Bowling Ball

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Physics 197 Lecture Notes - Lecture 19: Statics, Net Force, Bicycle Wheel

Physics 197 Lecture Notes - Lecture 20: Point Particle, Bowling Ball

Physics 197 Lecture 22: Oscillations: Simple Harmonic Motion

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Example: the total angular momentum of earth. Total angular momentum: for any system: (cid:1838)(cid:3047)(cid:3042)(cid:3047)=(cid:1838)+(cid:1838)(cid:3045)(cid:3042)(cid:3047)= + , (cid:1838)= = earth around the sun (365 days, (cid:1838)(cid:3045)(cid:3042)(cid:3047)= = earth around own axis (24 hours, torque causes changes in angular momentum. If a system is isolated (with no net external torque), angular momentum is conserved: angular momentum can be exchanged within a system between parts without the total angular momentum of the system changing. Calculating angular momentum: example 1: a cat standing on the edge of a turntable (both initially at rest) begins to walk along the edge of the turntable at 0. 6 m/s. The cat"s mass is 1/3 the mass of the turntable. At its closest point of approach, it is 3 m away from you. What is the ball"s angular momentum relative to your position: model: treat bowling ball as a sphere, ignore friction, apply conservation of angular momentum, visualize:

Related Questions

Earth is rotating about the Sun in our solar system. The distance between the Earth and Sun
is 1.5 × 1011m. Consider the impact of an asteroid of mass 8.9 ×1015 kg and a speed of 90,000
km/h with respect to the Earth’s surface. The asteroid strikes the Earth at the equator as shown
in Figure. Consider the mass and radius of the Earth are ME = 5.97 × 1024 kg and RE = 6.38
×106 m, respectively. Assume that the axial and orbital axis of rotations are parallel to each
other.

(a) Calculate the axial and total angular momentum of the Earth. (4 marks)
(b) What is the change in the angular velocity of the Earth due to the collision? (6 marks)
(c) What is the maximum possible change in the length of a day due to the collision?
(3 marks)
(d) How much energy is needed to stop the Earth’s rotation about its axis after the collision?
(4 marks)
(e) What would be the moment of inertia of the Earth if the axis of rotation is parallelly
shifted so that it touches the equator?

purpledog255

You are given a circular conducting wire loop with one
end cut out and connected to a resistor, R, as shown in
the figure to the right. A metal rod of length l is set at an
initial angle ?0 from the resistor, and then rotates
clockwise about the center of the wire loop with angular
frequency through a uniform magnetic field B
directed into the page. The metal rod stays in contact
with the wire loop at all points of its motion. Unless
otherwise requested, all answers should be in simplified
algebraic form using the above given variables.

(a) Given that the initial angle ?0 is in radians, what is theinitial area of the closed circuit âwedgeâdefined by ?0? (2pts.)
(b) What is the magnetic flux through this initial âwedgeâ areadefined by ?0? (2 pts.)
Starting at time t=0 at position ?0, the rod is rotated clockwisewith angular velocity as shown in
the figure. Given this configuration, answer questions (c)-(g)below:
(c) What is the direction of the induced magnetic field inside theâwedgeâ? (2 pts)
(d) What is the direction of the induced current around the closedcircuit? (2 pts)
(e) What is the magnitude of the induced emf, E in the circuit? (4pts)
(f) What is the magnitude of the induced current in the circuit? (4pts)
(g) What is the power used by the resistor? (4 pts)
(h) The metal rod is now rotated in the opposite direction, i.e. inthe counter-clockwise direction. Given this information, completethe chart below as to what quantities you just calculated change,and what ones do not change. You do not have to show work, justgive the result. No partial credit will be given here. (5pts)

Direction of induced magnetic field inside the âwedgeâ.
Direction of the induced current around the closed circuit.
Magnitude of the induced emf, E in the circuit.
Magnitude of the induced current in the circuit.
Power used by the resistor.

The setup is now modified slightly so that the circular conductingwire loop no longer has a small
section removed as shown in both figures below. This modificationwould allow the metal rod to
continuously rotate on the circular wire loop as clearlyillustrated in the 3D side view. The metal rod
is rotated clockwise, as in the initial part of the problem.

(i) Given this information, complete the chart below. You do nothave to show work, just give the
result. No partial credit will be given here. (5 pts)

Direction of induced magnetic
field inside the âwedgeâ.
Direction of the induced current
around the closed circuit.
Magnitude of the induced emf, E in
the circuit.
Magnitude of the induced current
in the circuit.
Power used by the resistor.

Physics 197 Lecture Notes - Lecture 20: Point Particle, Bowling Ball

Physics 197 Lecture Notes - Lecture 19: Statics, Net Force, Bicycle Wheel

Physics 197 Lecture Notes - Lecture 20: Point Particle, Bowling Ball

Physics 197 Lecture 22: Oscillations: Simple Harmonic Motion

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