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