Common Exam 2
8:30-9:45 am Friday, Oct. 29th (Arrive by 8:15 am)
Room: TBA
Bring scientific calculators and photo ID
Chapters B1: Ch. 4 ; B2: Ch. 6
To combat cheating, while taking the exams
1) students must show their ID upon entering the classroom,
2) no cell phone use,
3) if a student leaves the room during test time, e.g.Men’s/Ladies’ room,
he/she forfeits finishing the exam.
Old exmas are posted on web.
http://web.njit.edu/~kenahn
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Last Class…
B2. Ch6. Sec.1-2 : Circular Motion
Uniform Circular Motion
Today..
Non-uniform circular Motion
Oth Application
Other
A li ti of
f Newton’s
N t ’ Laws
L
(B.2,
(B 2 Ch
Ch.6,
6 S
S.3-4)
3 4)
2
Non-Uniform circular motion
Changing speed, or,
changing magnitude of velocity
Motion along a circle:
Changing direction of velocity
Why do we study non-uniform
circular motion?
Some exciting motions
are non-uniform circular motions!
Example Æ
3
1
Uniform
Cicular motion
An object moving along a circular path with a
constant speed:
Æ Only radial acceleration
Æ Net force directed toward the center of a
curvature (circle).
Non-uniform
Circular motion
An object moving along the circular path with a
changing speed :
Æ Both radial and tangential
g
accelerations
Æ Net force NOT directed toward the center of a
curvature (circle).
Radial acceleration: changing direction
Tangential acceleration: changing speed
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Even for Non-Uniform circular motion,
Radial component of acceleration
ar =
v2
r
Radial component of net force
Fr = m
v2
r
Radial components follow the same relations
as uniform circular motions!
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iClicker Quiz
For the roller coaster,
the magnitude of normal force at A is _______ mg.
(a) equal to
(b) less than
(c) greater than
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2
Example
A roller coaster of mass m=1000 kg is passing point A at 30 m/s.
Find the magnitude of normal force.
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iClicker Quiz
For the roller coaster,
the magnitude of normal force at B is _______ mg.
(a) equal to
(b) less than
(c) greater than
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Example
A roller coaster of mass m=1000 kg is passing point B.
Find the maximum speed it can have without losing contact with
the track.
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3
Example: A ball of mass 0.5 kg attached to a rope is rotating
in a vertical plane. What is the minimum speed the ball should have
at the top to prevent the rope from becoming loose?
iClicker Quiz: At the bottom,
the tension is ____ mg
(a)
(b)
(c)
(d)
equal to
less than
greater than
not enough information !!!
10
More application of Newton’s Laws
Common Procedure
1. Represent the object with a solid dot
2. Identify forces on the object and represent them with arrows
(Look for forces perpendicular to each other)
3. Prof. Ahn’s secret step: If you know, represent the direction of
acceleration with a different kind of arrow.
4. Choose x and y axis
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axis, so that maximum number of arrows point along the
x or y axis. (Choosing axis along the acceleration is often a good idea)
5. If a force points between x and y axis, see if you can identify the
angle. (Be ready to use your trigonometry skill.)
6. If acceleration is zero along an axis, forces are balanced along that
direction.
7. If acceleration is not zero along an axis, apply Newton’s second law
8. Solve the equation(s). Use formulas.
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iClicker Quiz
Net force on the object is
(a) zero.
(b) Not zero.
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