ROTATION
Monica Buckley
BIG IDEAS
*Angular
Displacement, velocity, and acceleration
o Angular Position
S = r
o One radian is the angle subtended by an arc length equal to the radius of the arc.
o
One radian equals 57.3 degrees. To convert from degrees to radians multiply
the number of degrees by 
/ 180.
o Angular Displacement
= 
- 
o
Average angular speed 
(omega) is the ratio of the angular displacement divided by the displacement in
the time interval t.
o Instantaneous angular speed 
(omega) is defined as the limit of the ratio change in angular displacement divided by change in time as
change in time approaches zero. 
(Units are
radians/second)
o Average Angular acceleration 
(alpha) is equal to the ratio of angular velocity divided by time.
o Instantaneous angular acceleration is the
limit of the ratio of angular velocity divided by time as time approaches
zero. 
o When rotating around a fixed axis it is important to remember that every particle on a rigid object rotates through the same angle and has the same angular speed and same angular acceleration.
*
Rotational Motion Constant Angular Acceleration
o
The Kinematic equations for rotational and linear
motion under constant acceleration are the same as the
linear kinematic equations except the variable are
, 
, and 
.
*Angular
and Linear quantities
o This section explains the relationship between linear and angular motion.
o Relationship between linear and angular speed
V = 
(r is the radius)
o Relationship between linear and angular acceleration (tangential)
a = 
o Relationship between linear and angular acceleration (radial)
a = 
*Rotational Energy
o Kinetic energy must include both rotational and linear energy
o The total kinetic energy is the sum of the kinetic energies of particles.
o
K = 
( 
) 
o The expression within the parentheses is known as the moment of inertia.
o
K = 
*Calculation of Moments of
Inertia
o
o Parallel-axis theorem: the moment of inertia about any axis parallel to and a distance D away from this axis is I = I + MD
*Torque
o The tendency of a force to rotate an object about some axis is measured by a vector quantity called torque.
o
*Relationship between Torque
and Angular Acceleration
o
o The torque acting on the particle is proportional to its angular acceleration.
*Work, Power, and Energy in Rotational Motion
o The radial component of F does no work because it is perpendicular to the displacement
o
o
o
Angular Momentum L=
STUDY TIPS & Test Prep
- Know and understand all equations in chapter 10
- Understand the relationship between linear and angular motion (equations on page 297)
- Understand how to use the moment of inertia to find the rotational kinetic energy
- Be familiar with the parallel axis theorem
- Know the difference between rad/sec and rev/ seconds and how to calculate the period
- Answer the quick quizzes in the reading. The answers to them are right after the problems.
- Remember the conservation of energy theorem
- Know how to do problems involving pulleys
- Review and understand all of the examples in the chapter—questions on the test and quizzes are similar.
- Don’t forget what you learned in previous chapters, the tests are cumulative.
- Make sure that you do and understand the review sheet and AP review problems before the test—it is very helpful for the test.
- BREAK DOWN THE PROBLEM
WEBSITE
LINKS
- http://www.slcc.edu -- this website explains rotation and includes many helpful diagrams to explain key concepts.
- http://www.brookscole.com-- this website is the companion website to the physics textbook. It is useful for all chapters, not just this one. It gives a brief description of the chapter, provides example problems and even gives solutions to some homework problems!!!!!!!
EXAMPLE PROBLEMS
1. A
disk of radius 20 cm rotates at a constant angular velocity of 6 radians per
second. How fast does a point on the
rim of this disk travel (in meters per second)?
Use the equation V = 
to relate linear and angular velocity. Then convert 20 cm to .2 meters.
V = 
= (.2m) (6 rad/s) = 1.2 m/s
- Derive
the expression for centripetal acceleration in terms of angular
speed.
a=
v
- A
bicycle wheel rotates at a constant angular acceleration of 2 rad/ second/
second. If the angular speed is 1
rad/ second at t=0, what angle does it rotate through in five
seconds?
Use kinematic equations for rotational motion since acceleration is constant.
SOLVE!!!!
- A
student pulls down on a rope that winds around a pulley with a force of 40
N. The radius of the pulley is 5
cm. Calculate the torque.
= (.05 m) (40 N) = 2 N m
- An
object of mass .5 kg moving in a circular path of radius .25 m experiences
a centripetal acceleration of 9 m/ second squared. Calculate angular speed.
Use equation found in number two to solve this problem.
- A wheel with a moment of inertia of 80 km times meters squared rotates on a fixed rigid axis at 600 rev/ min. What is its kinetic energy?
Use this equation to solve K = 
- What is the angular speed of the minute’s hand of a clock?
