Physics 211
Lecture 3
Today’s Concepts:
a) Relative motion
b) Centripetal acceleration
Relative Motion
Demo: tractor on paper
What is Mike’s velocity relative to the ground?
What you just did
v ac  v ab  v bc
v M ike ,G round  v M ike ,Train  vTrain ,G round
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Student Suggestion
Maybe we could also try to do relative motion like this: Find the velocity of
A wrt D, given the velocity of A wrt B, B wrt C, and C wrt D. I don't know something tricky.
You are flying east on an airplane, that is traveling 150 m/s due east w.r.t. the air.
There is a 30 m/s wind that is traveling due west w.r.t the ground.
You carry your food tray toward the back of the plane with a speed of 3 m/s w.r.t.
the plane.
How fast are you moving relative to the ground?
A) 183 m/s
B) 177 m/s
C) 123 m/s
D) 117 m/s
Vyou,ground = Vyou,plane + Vplane,air + Vair,ground
Vyou,ground = -3 m/s + 150 m/s -30 m/s = 117 m/s
East
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Prelecture 3, Question 1 (Reds POV)
I find it difficult to consider one moving object in the reference frame
of another, especially trying to determine which object is moving in a
positive direction.
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Prelecture 3, Question 1 (Reds POV)
X=+
I find it difficult to consider one moving object in the reference frame
of another, especially trying to determine which object is moving in a
positive direction.
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Prelecture 3, Question 1 (Reds POV)
Xo = - 12 m
X=+
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Prelecture 3, Question (Green’s POV)
Red
Green
Green
Red ball starts to the right (positive) and comes closer to green (origin)
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Checkpoint
A girl stands on a moving sidewalk that moves to the right at 2 m/s
relative to the ground. A dog runs toward the girl in the opposite direction
along the sidewalk at a speed of 8 m/s relative to the sidewalk.
What is the speed of the dog relative to the ground?
vdog,belt = 8 m/s
vbelt,ground = 2 m/s
A) 6 m/s
B) 8 m/s
C) 10 m/s
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What is the speed of the dog relative to the ground?
vdog,belt = 8 m/s
vbelt,ground = 2 m/s
A) 6 m/s
B) 8 m/s
C) 10 m/s
+x
vdog, ground = vdog, belt + vbelt, ground
= (-8 m/s) + (2 m/s) = -6 m/s
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Checkpoint
A girl stands on a moving sidewalk that moves to the right at 2 m/s
relative to the ground. A dog runs toward the girl in the opposite direction
along the sidewalk at a speed of 8 m/s relative to the sidewalk.
What is the speed of the dog relative to the girl?
vdog,belt = 8 m/s
vbelt,ground = 2 m/s
A) 6 m/s
B) 8 m/s
C) 10 m/s
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What is the speed of the dog relative to the girl?
vdog,belt = 8 m/s
vbelt,ground = 2 m/s
A) 6 m/s
B) 8 m/s
C) 10 m/s
Using the velocity formula:
vdog, girl = vdog, belt + vbelt, girl
= -8 m/s + 0 m/s
= -8 m/s
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Tractor Demo (moving cardboard)
Which direction should I point the toy bulldozer to get it
across the cardboard fastest?
A) To the left
B) Straight across
C) To the right
A B C
ACT
A man starts to walk along the dotted line painted on a moving sidewalk toward
a fire hydrant that is directly across from him. The width of the walkway is 4
m, and it is moving at 2 m/s relative to the fire-hydrant. If his walking speed
is 1 m/s, how far away will he be from the hydrant when he reaches the
other side?
A) 2 m
B) 4 m
C) 6 m
D) 8 m
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If the sidewalk wasn’t moving:
Time to get across:
Dt = distance / speed
= 4m / 1m/s
=4s
v man , sidewalk
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Just the sidewalk:
v sidew alk , hydrant
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Combination of motions:
v m an , hydrant  v m an , sidew alk  v sidew alk , hydrant
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D
D = (speed of sidewalk) ∙ (time to get across)
=
(2 m/s)
∙
(4 s)
= 8m
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ACT
Three swimmers can swim equally fast relative to the water. They
have a race to see who can swim across a river in the least time.
Relative to the water, Beth swims perpendicular to the flow, Ann
swims upstream at 30 degrees, and Carly swims downstream at
30 degrees.
Who gets across the river first?
Ann
A) Ann B) Beth C) Carly
Beth
Carly
y
x
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Look at just water & swimmers
Time to get across = D / Vy
B
D
A
C
30o 30o
Vy,Beth = Vo
y
Vy,Ann = Vocos(30o)
x
Vy,Carly = Vocos(30o)
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ACT
Three swimmers can swim equally fast relative to the water. They
have a race to see who can swim across a river in the least time.
Relative to the water, Beth swims perpendicular to the flow, Ann
swims upstream at 30 degrees, and Carly swims downstream at
30 degrees.
Who gets across the river second?
A) Ann B) Carly C) Both same
Ann
Carly
y
x
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Checkpoint (& Demo: tether ball)
A girl twirls a rock on the end of a
string around in a horizontal circle
above her head as shown from above
in the diagram.
A
B
If the string breaks at the instant
shown, which of the arrows best
represents the resulting path of the
rock?
C
D
Once the string breaks, there is no longer
any centripetal force exerted on the rock by
the string, and so the rock continues in a
straight path tangent to the point at which
the string broke.
Top view looking down
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Demo: water in bucket
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Centripetal Acceleration
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Angular Velocity w
v = wR
w is the rate at which the angle q changes:
dq
w
dt
q
Once around:
v  Dx / Dt = 2pR / T
w  Dq / Dt = 2p / T
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Angular Velocity w
v = wR
Another way to see it:
dq
R
v dt =R dq
dq
vR
dt
v = Rw
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Earth’s Rotation
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Earth’s Rotation
When standing on the equator, what is the direction of your acceleration due to the
rotation of the earth?
A)
B)
C)
D)
E)
East
West
Toward Center of Earth
Away from Center of Earth (toward sky)
North
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