Advanced/Notes 8.5

Section 8.5 and 8.6Rotational Dynamics; Torque and Rotational Inertia

Rotational DynamicsHow do I define and calculate

moment of inertia?

How do I solve rotational dynamic problems?

Deriving a Force EquationSay we have a

point mass, m

Force F is applied

Using and and

Moment of Inertiamr2 is called the rotational inertia

of an object

Also called the moment of inertia (I)

So

Rotational InertiaDistribution of mass mattersSame massLeft has a greater rotational

inertia, since most of its mass is far away from the axis of rotation

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.

Moments of Inertia• I depends

on mass distribution

• I depends on location of axis

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.

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.

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.

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

HomeworkRead Sections 8.5 and 8.6Do Problems # 27 - 32, page 220

HomeworkPage 221, # 33 – 37, 42