Chapter 8 Rotational Motion

The first 7 chapters of the text ignore any possible rotation of objects. In the real world rotation is a significant part of many motions, so we will be studying rotation. The good (or bad) news is that the equations and methods used to analyze motion in the first part of the text are very, very similar to the methods used to analyze rotation. The vector nature of rotation is very interesting and unexpected, but we don’t have time to study it on MWF. The 161 group will do the interesting vector analysis in our 8am Tuesday session. 151 students are always invited to attend!

Terms you should know after reading this section: radian

angular velocity angular acceleration

frequency period

1. TRUE or FALSE In a rotating system, the standard unit of angular measure is the degree.

2. TRUE or FALSE Angular velocity is identical to linear velocity.

3. Imagine that a meter stick is mounted horizontally with one end on an axis. The meter stick then rotates around the axis.

a) TRUE or FALSE All parts of the meter stick have the same angular velocity.

b) TRUE or FALSE All parts of the meter stick have the same linear velocity.

4. TRUE or FALSE Angular acceleration is the same as centripetal acceleration.

The mathematical form of these equations (page 215) should look familiar.

5. In a certain music CD player, the CD reaches an angular speed of 500 revolutions per minute. This angular speed is obtained 5 seconds after the unit is turned on. What is the value of the angular acceleration?

6. How many revolutions did the CD make during these first 5 seconds?

7. TRUE or FALSE For the case of rolling motion without slipping the point of contact with the ground is at rest with respect to the ground.

What is the relationship between linear velocity and angular velocity? see page 211

Terms you should know: lever arm axis of rotation

line of action of a force

**** Observe rotation by applying a torque to a ruler which is suspended by a paperclip. Then answer the questions below.

8. TRUE or FALSE The amount of torque applied to an object does not depend on where the (constant) force is applied to the object.

9. TRUE or FALSE The amount of torque applied to an object does not depend on the angle between the line of action of the force and the lever arm.

10. TRUE or FALSE If the net force on an object is non-zero the torque on the object will be non-zero.

Terms: moment of inertia rotational inertia

11. TRUE or FALSE The constant of proportionality between the torque and the angular acceleration is called the moment of inertia.

12. TRUE or FALSE The value of the moment of inertia only depends on the mass of the object.

A photocopy of the table on page 223 will be given to you at the next test.

Terms: rotational kinetic energy

13. TRUE or FALSE Conservation of Energy principles cannot be used in problems that involve rotation.

Translational, or linear, kinetic energy is computed with ½ m v² where v is the velocity of the center of mass. The center of mass of an object which is rotating on a fixed axis does not move but the object does have kinetic energy, rotational kinetic energy ½ I w² .

14. TRUE or FALSE The rotational kinetic energy of an object cannot be larger than the translational kinetic energy of the object.

15. A hoop and a solid disk are placed at the same height above a table on a ramp. The objects have the same mass and the same radius. When the objects are released from rest, the disk will reach the bottom of the ramp first.

16. If the solid disk in question 2 has a larger mass than the hoop, the hoop may reach the bottom of the ramp first.

Terms: angular momentum

Conservation of Angular Momentum

17. TRUE or FALSE If the net external torque applied to an object is equal to zero then the angular momentum of the object will be a constant.

18. TRUE or FALSE The torque caused by the force of gravity from the sun on a planet causes the planet to speed up as it passes near the sun in its elliptical orbit.

8.9 Vector Nature of Angular Quantities 161 only

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