PHYS 1003 Lecture Notes - Lecture 15: Rotational Energy, Moment Of Inertia, Cross Product

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10 Nov 2016

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The torque is the cross product of the distance from the centre of rotation and the force. Point fingers on right hand in direction of vector a. Curl fingers in direction of vector b. Thumb indicates direction of the cross product - vector c. The si unit of torque is the newton. metre, n. m. ** note that it is always written as newton. metre or n. m to identify it as a rotational unit. For example, torque and work are not equivalent quantities, even though they have the same units this is because torque is a vector quantity and work/energy is a scalar quantity . The work done by a constant torque can be defined in terms of the angular displacement. If the torque produces an angular displacement. Integrate the torque function with respect to the angle. ** note that this is very similar to the work done by a variable force concept.

Related Questions

1. An object is dropped from a height.Once it is moving,which ofthe following statements are true,at least at one point?
a)its velocity is more than its accelerations
b)its velocity is less than its acceleration
c)its velocity is the same as its acceleration
d)its velocity is never equal to its acceleration

2. Which type of quantity is characterized by both magnitude anddirection?
a)scalar
b)vector
c)trigonometric
d)algebraic variable

3. A hiker walks 200m west and then walks 100m north. In whatdirection is her resulting displacement?
a)north
b)west
c)northwest
d)none of the answer is correct

4. Vector 1 is 7 units long and is at 70 degree. Vector 2 is 5units long and is at 225 degree. Vector 3 is a 3 units long and isat 150 degree. Which vector has equal magnitude components?
a)Vector 1
b)vector2
c)vector 3
d)none of the vectors has equal magnitude components??????

5. Which of the following is an example of the type of force thatacts at a distance?
a)gravitational
b)magnetic
c)electrical
d)all of the above

6. A crate weight W is being pushed across a horizontal surface bya force directed at an angle of 20 degrees below the horizontal.What is the magnitude of the normal force on the crate?
a)it is less then W
b)it equals W
c)it is more than W
d)none of the above since the coefficient of kinetic friction isnot given

7. The net force on an object is in the positive x-direction.Consider the following statements.
(i) The object can be moving in the negative x-direction.
(ii) The object can be speeding up.
(iii) The object can be slowing down.
(iv) The object can be moving in the positive y-direction.

Which of the statements are true?
a. (i) and (ii)
b. (ii) and (iii)
c. (iii) and (iv)
d. Choose this answer if all the statements are true.

8.The work done by static friction can be:
a. positive.
b. negative.
c. zero.
d. Any of the above.

9.The rate at which work is done is equivalent to which of thefollowing?
a. increase in potential energy
b. thermal energy
c. potential energy
d. power

10.The dimensional equivalent of the quantity impulse in terms ofthe fundamental quantities (mass, length,
time) is which of the following?
a. MLT-1
b. ML2T-2
c. MLT
d. MLT-2

11. The dimensional equivalence of the quantity "momentum" in termsof the fundamental quantities (mass,
length, time) is:
a. MLT-1.
b. ML2T-2.
c. MLT.
d. MLT-2.

12.In order for a satellite to be geosynchronous, its orbitmust:
a. go over the North and South Poles.
b. be over the equator.
c. be over a single longitude.
d. emit television signals.

13. The quantity "angular momentum" (in terms of the fundamentalquantities of mass, length, and time) is equivalent
to:
a. MLT-2.
b. ML2T-1.
c. ML2T-3.
d. ML3T.
d. MLT-2.

Learning Goal: To work through astraightforward application of Faraday's law to find the EMF andthe electric field surrounding a region of increasing flux

Faraday's law describes how electric fields and electromotiveforces are generated from changing magnetic fields. This problem isa prototypical example in which an increasing magnetic fluxgenerates a finite line integral of the electric field around aclosed loop that surrounds the changing magnetic flux through asurface bounded by that loop. A cylindrical iron rod withcross-sectional area is oriented with its symmetry axis coincidentwith the z axis of a cylindrical coordinate system as shown. It hasa uniform magnetic field inside that varies according to . In otherwords, the magentic field is always in the positive z direction,and it has no other components.

For your convenience, we restate Faraday's law here: , where is theline integral of the electric field, and the magnetic flux is givenby , where is the angle between the magnetic field and the localnormal to the surface bounded by the closed loop.
Direction: The line integral and surface integral reverse theirsigns if the reference direction of or is reversed. The right-handrule applies here: If the thumb of your right hand is taken along ,then the fingers point along . You are free to take the loopanywhere you choose, although usually it makes sense to choose itto lie along the path of the circuit you are considering.

Find , the electromotive force (EMF) around a loop that is atdistance from the z axis, where is restricted to the region outsidethe iron rod as shown. Take the direction shown in the figure aspositive.
Express in terms of , , , , and any needed constants such as , ,and .
Due to the cylindrical symmetry of this problem, the inducedelectric field can depend only on the distance from the z axis,where is restricted to the region outside the iron rod. Find thisfield.
Express in terms of quantities given in the introduction (andconstants), using the unit vectors in the cylindrical coordinatesystem,r^ ,theta^ , and z^ .

PHYS 1003 Lecture Notes - Lecture 15: Rotational Energy, Moment Of Inertia, Cross Product

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