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CHAPTER 11: Rotation
Veronica Sikka, Woon Chow, Phan Tran
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*Denotes problem that may be on the Exam |
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Synopsis
Chapter eleven begins the study of rotational motion. This chapter focuses on
pure rotational motion, or rotation without translation. The pattern of this
chapter is very similar to the contents from chapter two to chapter eight.
Instead of trying to think of this chapter as new topics, try to make links to
the previous material. The chapter includes concepts of rotational kinematics,
kinetic energy of rotation, rotational inertia, torque, and Newton's second law
for rotation.
A Helpful Link on Torque
Summary
Major Concepts
Refer to the definition section for more detailed explainations of the
terms
Rotational Variables
- Angular Position
- Angular Velocity
- Angular Acceleration
Rotational Kinematics
- Refer to Table 11-1 in textbook
Relating the Linear and Angular Variables
- Position (s = qr)
- Velocity (v = wr)
- Tangential Acceleration (at = ar)
- Radial Acceleration (ar = v2/r = w2r)
Rotational Inertia
- Refer to Table 11-2 in textbook
Parallel-Axis Theorem
Torque
- Vector quantity
- Force-distance units
Newton's second law in angular form
Work and Rotational Kinetic Energy
- DK = 1/2Iwf2
- 1/2Iwi2
= W
Problem Types
- Rotation with constant angular acceleration
- Relations between linear & angular variables
- Rotational inertia
- Torque
- Newton's second law in angular form
- Work &rotational kinetic energy
Important Notes
- Put Table 11-1, 11-2, and 11-3 on cheat sheet for the exam!
- Always use radians when using angular positions, angular
velocities, and angular accelerations. Values in degrees will not work!
- Don't waste time trying to learn the material by thinking it is brand-new
material. Take time to connect this chapter with previous chapters. Review
those chapters if necessary. Most equations in this chapter have the same
form as their linear counterpart. Note these similarities.
Important Terms
- angular displacement change in the angular position of the
reference line from q1 to q2
(Dq = q2 - q1)
- angular position (q) way of describing
the motion of a rotating body that is found by measuring the angle of the
reference line relative to a fixed direction (q =
s / r)
- angular speed (w) magnitude of an
angular velocity
- average angular acceleration change in angular velocity of a
rotating body over a time interval (a = Dw
/ Dt)
- average angular velocity change in the angular position over a time
interval (w = Dq / Dt)
- instantaneous angular acceleration change in angular velocity at an
instant in time (a = dw
/ dt)
- instantaneous angular velocity change in the angular position at an
instant in time (w = dq
/ dt)
- line of action extended line running through the F vector to
which the moment arm is measured
- moment arm perpendicular distance between the rotation axis and an
extended line running through the F vector
- Newton's 2nd Law in angular form rotational analog of Newton's 2nd
law (St = Ia)
- Parallel-Axis Theorem given the rotational inertia of a body about
any axis that passes through its center of mass, the rotational inertia
about any other axis parallel to that axis can be found according to the
equation I = Icm + Mh2
- radians unit used with angles in problems involving rotation
- reference line line that is perpendicular to the rotation axis,
fixed in the rigid body, and rotating with the body
- rotation axis fixed axis about which a rigid body is rotated
- rotational inertia (moment of inertia) the distribution of mass of
a rotating body about its axis of rotation
- torque force acting on a body that produces rotation; defined as
the product of the force times the perpendicular distance from the pivot
point to the force (t = (r)(F sin j))
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