When the ball reaches the break in the circle, which …...For uniform circular motion, the...
Transcript of When the ball reaches the break in the circle, which …...For uniform circular motion, the...
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When the ball reaches the break in the
circle, which path will it follow?
Checking Understanding:
Circular Motion Dynamics
Slide 6-21
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Answer
When the ball reaches the break in the
circle, which path will it follow?
C.
Slide 6-22
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A coin sits on a rotating
turntable.
At the time shown in
the figure, which arrow
gives the direction of
the coin’s velocity?
Additional Questions
Slide 6-45
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Answer: A
A coin sits on a
rotating turntable.
At the time shown in
the figure, which arrow
gives the direction of
the coin’s velocity?
A
Slide 6-46
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A coin sits on a
rotating turntable.
At the instant shown,
suppose the frictional
force disappeared. In
what direction would
the coin move?
Additional Questions
Slide 6-49
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Answer
A
A coin sits on a
rotating turntable.
At the instant shown,
suppose the frictional
force disappeared. In
what direction would
the coin move?
Slide 6-50
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When a ball on the end of a string is swung
in a vertical circle, the ball is accelerating
because
A. the speed is changing.
B. the direction is changing.
C. the speed and the direction are
changing.
D. the ball is not accelerating.
Checking Understanding
Slide 6-13
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Answer
When a ball on the end of a string is swung
in a vertical circle, the ball is accelerating
because
A. the speed is changing.
B. the direction is changing.
C. the speed and the direction are
changing.
D. the ball is not accelerating.
Slide 6-14
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For the ball on the end of a string moving in
a vertical circle:
What is the direction of the net force on the
ball?
A. tangent to the circle
B. toward the center of the circle
C. there is no net force
Checking Understanding:
Circular Motion Dynamics
Slide 6-19
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Answer
For the ball on the end of a string moving in
a vertical circle:
What is the direction of the net force on the
ball?
A. tangent to the circle
B. toward the center of the circle
C. there is no net force
Slide 6-20
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For the ball on the end of a string moving in
a vertical circle:
What force is producing the centripetal
acceleration of the ball?
A. gravity
B. air resistance
C. normal force
D. tension in the string
Checking Understanding:
Circular Motion Dynamics
Slide 6-17
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Answer
For the ball on the end of a string moving in
a vertical circle:
What force is producing the centripetal
acceleration of the ball?
A. gravity
B. air resistance
C. normal force
D. tension in the string
Slide 6-18
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A coin sits on a
rotating turntable.
At the time shown in
the figure, which
arrow gives the
direction of the
frictional force on the
coin?
Additional Questions
Slide 6-47
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Answer
A coin sits on a
rotating turntable.
At the time shown in
the figure, which
arrow gives the
direction of the
frictional force on the
coin?
D
Slide 6-48
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Reading Quiz
For uniform circular motion, the acceleration
A. is parallel to the velocity.
B. is directed toward the center of the
circle.
C. is larger for a larger orbit at the same
speed.
D. is always due to gravity.
E. is always negative.
Slide 6-6
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Answer
For uniform circular motion, the acceleration
A. is parallel to the velocity.
B. is directed toward the center of the
circle.
C. is larger for a larger orbit at the same
speed.
D. is always due to gravity.
E. is always negative.
Slide 6-7
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Summary
Slide 6-41
Speed = v = Δd/Δt = 2πr/T
at radius, r,
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When a ball on the end of a string is swung
in a vertical circle:
What is the direction of the acceleration of
the ball?
A. Tangent to the circle, in the direction
of the ball’s motion
B. Toward the center of the circle
Checking Understanding
Slide 6-15
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Answer
When a ball on the end of a string is swung
in a vertical circle:
What is the direction of the acceleration of
the ball?
A. Tangent to the circle, in the direction
of the ball’s motion
B. Toward the center of the circle
Slide 6-16
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Angular Displacement, , and Angular Velocity, ω
is the angle between position 1 and 2.
is the amount of rotation—measured in degrees or radians (we’ll use radians since they are the SI unit for ).
1
2
r
For an object rotating about a fixed axis, the angular displacement, , is the angle swept out by a line passing through any point on the body and intersecting the axis of rotation perpendicularly. By convention, the angular displacement is positive if it is counterclockwise.
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Angular Displacement,
For an object rotating, angular displacement is found by:
(in radians) = Arc length = s
= f – i where i is sometimes zero.
radius r
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If determining for a complete circle, or one complete cycle:
Arc length = 2r (for one revolution)
= (arc length) / r
= (2r) / r = 2 radians
1 revolution = 2 radians = 360o
So, 1 radian = 360o / 2 = 57.3o
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UNIFORM CIRCULAR MOTION (UCM)
Angular displacement = Δθ = the angle displaced, measured in radians, while an object undergoes UCM
Δθ= ω Δt
Angular Velocity = ω (Greek: Omega)
ω = 2 π f and ω = Δθ/Δt
All points on a rotating object rotate through the same angle in the same time, and have the same frequency. Angular velocity is also known as the turning rate.
Angular velocity: all points on a rotating object have the same angular velocity, ω, (same turning rate) but different speeds, v, and v =ωr, depending on the location of that point.
v =ωr
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ω is positive if object is rotating counterclockwise. (Negative if rotation is clockwise.)
Conversion: 1 revolution = 2 π rad
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Angular Velocity Angular Velocity = the “turning rate”—expressed in units of
revolutions per second, or metric: radians per second.
Angular velocity = angular displacement / elapsed time
= /t units: radians/second or rad/s
For one cycle: t = T = period = time for one cycle
And, =s/r= (2r)/r = 2 radians = angular
displacement for one cycle
= /t = 2 radians / T = 2 / T
= 2/T And since T=1/f , where f = frequency
= 2 / (1/f) = 2f
= 2f Angular velocity is sometimes called angular frequency!
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Checking Understanding
Two coins rotate on a turntable. Coin B is twice as
far from the axis as coin A.
A. The angular velocity of A is twice that of B.
B. The angular velocity of A equals that of B.
C. The angular velocity of A is half that of B.
Slide 7-13
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Answer
All points on the turntable rotate through the
same angle in the same time. ω = θ/ tAll points have the same period, therefore, all
points have the same frequency.
ω = 2 π f
Two coins rotate on a turntable. Coin B is
twice as far from the axis as coin A.
A. The angular velocity of A is twice
that of B.
B. The angular velocity of
A equals that of B.
C. The angular velocity of A is half
that of B.
Slide 7-14
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Important to realize… Angular velocity, , or the “turning rate” is the same everywhere on the rotating body/object, b/c /t =2/T is the same.
But, instantaneous velocity, the velocity tangent to the circular path—called tangential velocity, vT– is greater for points (places) farther from the axis.
The magnitude of the tangential velocity is referred to as the tangential speed.
v=d/t = 2r/T = 2rf
vT= r
vT
VT
vT
vT
© 2010 Pearson Education, Inc.
Two coins rotate on a turntable. Coin B is
twice as far from the axis as coin A.
A. The speed of A is twice that of B.
B. The speed of A equals that of B.
C. The speed of A is half that of B.
Checking Understanding
Slide 7-15
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Answer
Twice the radius means twice the speed, v.
Therefore, B moves with twice the speed of A.
Two coins rotate on a turntable. Coin B is
twice as far from the axis as coin A.
A. The speed of A is twice that of B.
B. The speed of A equals that of B.
C. The speed, v, of A is
half that of B.
Slide 7-16
v rw=
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Uniform Circular Motion
Slide 6-23
From:vT= r = 2 π r fac =
a = ac
v = vT
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Circular MotionAnd v = 2πrf =
tangential speed or
speed at that place (at r)
a = ac