Download - Advanced/Notes 8.5
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Section 8.5 and 8.6Rotational Dynamics; Torque and Rotational Inertia
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Rotational DynamicsHow do I define and calculate
moment of inertia?
How do I solve rotational dynamic problems?
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Deriving a Force EquationSay we have a
point mass, m
Force F is applied
Using and and
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Moment of Inertiamr2 is called the rotational inertia
of an object
Also called the moment of inertia (I)
So
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Rotational InertiaDistribution of mass mattersSame massLeft has a greater rotational
inertia, since most of its mass is far away from the axis of rotation
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ExampleTwo small weights, of mass 5.0 kg and 7.0 kg are mounted 4.0 m apart on a light rod(whose mass can be ignored). Calculate the moment of inertia fora) When rotated about
an axis halfway between the weights and
b) When rotated about an axis 0.50 m to the left of the 5.0 kg mass.
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Moments of Inertia• I depends
on mass distribution
• I depends on location of axis
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Problem Solving Steps
1. Draw a diagram.
2. Decide what the system comprises.
3. Draw a free-body diagram for each object under consideration, including all the forces acting on it and where they act.
4. Find the axis of rotation; calculate the torques around it.
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Problem Solving Steps 5. Apply Newton’s second law for rotation. If
the rotational inertia is not provided, you need to find it before proceeding with this step.
6. Apply Newton’s second law for translation and other laws and principles as needed.
7. Solve.
8. Check your answer for units and correct order of magnitude.
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Example
A 15.0 N force is applied to cord wrapped around a pulley of mass M = 4.00 kg and a radius r = 33.0 cm. The pulley accelerates uniformly from rest to an angular speed of 30.0 rad/s in 3.00 s. If there is a frictional at the axel, determine the moment of inertia of the pulley.
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Example by steps
1) Diagram: Given2) System: pulley
and cord3) Free-body
diagram: Given4) Axis of Rotation,
torques, and positive direction
5) Newton’s Laws
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HomeworkRead Sections 8.5 and 8.6Do Problems # 27 - 32, page 220
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HomeworkPage 221, # 33 – 37, 42