This document discusses rotational dynamics and torque. It defines moment of inertia as relating to how mass is distributed about an axis of rotation. Greater moment of inertia means more mass is farther from the axis. Examples calculate moment of inertia for different axes of rotation for a system with two masses on a rod. Solving rotational dynamics problems involves drawing diagrams, identifying the system and forces, finding the axis of rotation, applying Newton's laws for rotation and translation, and checking units and magnitudes. The associated homework assignments problems 27-32 and 33-37, 42 are also listed.

1. Section 8.5 and 8.6
Rotational Dynamics; Torque and Rotational
Inertia

2. Rotational Dynamics
 How do I define and calculate moment
of inertia?
 How do I solve rotational dynamic
problems?

3. Deriving a Force Equation


4. Moment of Inertia


5. Rotational Inertia
 Distribution of mass matters
 Same mass
 Left has a greater rotational
inertia, since most of its mass is far
away from the axis of rotation

6. Example
Two 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 for
a) 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.

7. Moments
of Inertia
• I depends
on mass
distribution
• I depends
on location
of axis

8. 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.

9. 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.

10. Example


11. Example by steps
1) Diagram: Given
2) System: pulley and
cord
3) Free-body diagram:
Given
4) Axis of
Rotation, torques, an
d positive direction
5) Newton’s Laws

12. Homework
 Read Sections 8.5 and 8.6
 Do Problems # 27 - 32, page 220

13. Homework
 Page 221, # 33 – 37, 42