Uniform Circular Motion (UCM) 4/25/07. Uniform Circular Motion UCM means that is constant Which...
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Transcript of Uniform Circular Motion (UCM) 4/25/07. Uniform Circular Motion UCM means that is constant Which...
Uniform Circular Motion (UCM)
4/25/07
Uniform Circular Motion
• UCM means that is constant
• Which means that…
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Uniform Circular Motion
• UCM means that is constant
• Which means that…– = 0
Uniform Circular Motion
• UCM means that is constant
• Which means that…– = 0
– aT = 0
Uniform Circular Motion
• UCM means that is constant
• Which means that…– = 0
– aT = 0
– |vT| = constant
Uniform Circular Motion
• UCM means that is constant
• Which means that…– = 0
– aT = 0
– |vT| = constant
• BUT… vT is not constant because the direction changes
Uniform Circular Motion
• If vT isn’t constant, this means there is an acceleration.
In which direction is the acceleration? Hint: what is exerting the force on the ball?
Uniform Circular Motion
• If vT isn’t constant, this means there is an acceleration.
If you let go of the string when the object is at the top of the arc, which way will the object go?
Centripetal Acceleration
• Centripetal = “Center-seeking”• Equation
ac =vT
2
r
But vT = r so
ac =(r)2
r= r2
Units{ac} = ?
Centripetal Acceleration
• Centripetal = “Center-seeking”• Equation
ac =vT
2
r
But vT = r so
ac =(r)2
r= r2
Units{ac} = ms2
Directions of Accelerations
Acceleration Direction
aT =vT
tvT
Directions of Accelerations
Acceleration Direction
aT =vT
tIn line with vT
vTaT
Directions of Accelerations
Acceleration Direction
aT =vT
tIn line with vT
vTaT
=f - o
tIn line with
Directions of Accelerations
Acceleration Direction
aT =vT
tIn line with vT
vTaT
=f - o
tIn line with
Directions of Accelerations
Acceleration Direction
aT =vT
tIn line with vT
vTaT
=f - o
tIn line with
ac =vT
2
r= r2 Towards center
Directions of Accelerations
Acceleration Direction
aT =vT
tIn line with vT
vTaT
=f - o
tIn line with
ac =vT
2
r= r2 Towards center
Centripetal Force
F = ma
Centripetal Force
Fc = mac = m vT2
r
or
Fc = mac = mr2
Centripetal Force
The centripetal force is the net force on an object in circular motion
vT
Centripetal Force
The centripetal force is the net force on an object in circular motion
vT
Centripetal Force
The centripetal force is the net force on an object in circular motion
vT
Example:
A child on a merry-go-round is 2.5 m from the center. The child weighs 40 kg and the centripetal force on the child is 160 N towards the center. Find vT.
2.5 m