PHYSICS 231 Lecture 16: Centripetal acceleration

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PHYSICS 231Lecture 16 Centripetal acceleration

• Remco Zegers
• Walk-in hour Thursday 1130-1330 am
• Helproom

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Last week...
Average angular velocity (rad/s)
Instantaneous Angular velocity
Average angular acceleration (rad/s2)
2? rad ? 3600 10 ? 2?/360 rad 1 rad ?360/2? deg
Instantaneous angular acceleration
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And...
Angular and linear velocity are related
Angular and linear acceleration are relation
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Rotational motion
Angular motion
?(t) ?(0)?(0)t½?t2 ?(t) ?(0)?t
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Driving a car through a bend
Is there a force that pushes you away from the
center of the circle?

• Newtons first law If no net force is acting on
  an object, it will continue with the same
  velocity (inertia of mass)
• Velocity is a vector (points to a direction)
• If no net force is acting on an object, it will
  not change its direction.
• A force is acting on the car (steeringfriction)
  but you tend to go in the same direction as you
  were going!
• It is not a force that pushes you, but the lack
  of it!
• The side door will keep you from falling out it
  exerts a force on you and you exert a force on
  the door (F21-F12)

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Centripetal acceleration
The change in velocity is not the change in
speed but in direction.
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Centripetal acceleration
acv2/r directed to the center of the circular
motion
Also v?r, so ac?2r

• This acceleration can be caused by various
  forces
• gravity (objects attracted by earth)
• tension (object making circular motion on a
  rope)
• friction (car driving through a curve)
• etc

This acceleration is NOT caused by a mysterious
force
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A race car accelerating on a track.
atangential
ac
atotal ?(ac2atangemtial2)
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Forces that can cause centripetal acceleration.
Object swinging on a rope.
T
?Fma Tmac Tmv2/rm?2r
T
An object with m1 kg is swung with a rope of
length 3 m around with angular velocity ?2
rad/s. What is the tension in the rope?
Tm?2r122312 N
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Lifting by swinging
Swinging mass (m1) with velocity v
What is the relation between v and r that will
keep m2 stationary?
v out of paper
r
a-m2g/m1
Hanging mass (m2)
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A car going through a bend
A car is passing through a bend with radius 100
m. The kinetic coefficient of friction of the
tires on the road is 0.5. What is the maximum
velocity the car can have without flying out of
the bend?
?Fma ?knmac ?kmgmv2/r 0.59.81v2/100 v22 m/s
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2001 A space odyssey
A space ship rotates with a linear velocity of 50
m/s. What should the distance from the central
axis to the crews cabins be so that the crew
feels like they are on earth? (the floor of
the cabins is the inside of the outer edge of the
spaceship)
?Fma mgmv2/r so rv2/9.8 and thus r255
m
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Conical motion
What is the centripetal acceleration if the mass
is 1 kg and ?20o?
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Horizontal direction ?Fmac Tsin?mac mgsin?/cos?
mgtan?mac acgtan?9.80.363.6 m/s2
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A general strategy

• As usual, make a drawing of the problem, if not
  given.
• Draw all the forces that are acting on the
  object(s) under investigation.
• Decompose each of these into directions toward
  the center of the circular path and perpendicular
  to it.
• Realize that ?Fto centermacmv2/r