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Notes for Test 5

**Chapter 8 **

Rotational Kinematics Concept Summary is on p. 239. You should know the definition of an angle in radians, Equation (8.1):

*s r r *

*s *

and how to use this equation to estimate distances. See Conceptual Example 2 and the example we did in class. You should know how to convert between the units of radians, degrees and revolutions using the conversion factors that will be provided on the test. See Example 3. You should be familiar with the definition of average angular velocity, Equation (8.2). See Example 3. You should also be familiar with the definition of average angular acceleration, Equation (8.4). See Example 4. You should know how to use the equations of rotational kinematics for the case of constant angular acceleration, Equations (8.4), (8.6), (8.7), (8.8). See Example 5, the examples we did in class and Quiz 5. You should know what is meant by

*tangential velocity*

and

*tangential acceleration*

. You should know how to use the formulas that relate these to angular velocity and angular acceleration, Equations (8.9) and (8.10), respectively. See Example 6. Know the relationships between centripetal acceleration, tangential velocity and angular velocity, Equations (8.11). See Example 7.

**Chapter 9**

Rotational Dynamics Concept Summary is on p. 276. You should know how the definition of torque, Equation (9.1) and the concept of the lever arm. You should be familiar with the three equations for rigid body equilibrium:

*F x*

0,

*F y*

0, 0 You should know how to use these to find forces or lever arms for a system in equilibrium. See Examples 3, 4 and 5 and the example we did in class. You should be familiar with the concept of center of gravity. See Examples 6 and 7. You should know Newton’s second law for rotational motion about a fixed axis:

*I*

,

where

*I*

is the

*moment of inertia*

of the rotating object about the fixed axis, its angular acceleration and the net torque on the object about the fixed axis. See Table 9.1, Examples 9 and 10. Be familiar with the equation for rotational work, Equation (9.8):

*W*

R where a constant torque rotates an object through an angle measured in radians. Be familiar with the equation for rotational kinetic energy, Equation (9.9): KE R 1 2

*I*

2 where is the object’s angular velocity and

*I*

its moment of inertia about the fixed axis it is rotating about. Know how to solve rolling problems using conservation of energy. See Example 13. Be familiar with the concept of angular momentum:

*L I*

and know how to solve problems relating to conservation of angular momentum. See Conceptual Example 14.