The following examples refer to Bradley's Calculus.
Asymptotes and limits involving infinity must also be considered when sketching curves.
Examples:
- pg. 212 (Section 3.6): #58
- pg. 219 (Section 3.7): #44, #45
Using many of the techniques already learned, one can solve practical optimization problems
Examples:
- pgs. 225-226 (text)
- pg. 228 (Section 3.7): #26, #28
- pg. 229 (Section 3.7): #32, #33
The following examples refer to Young and Freedman's University Physics.
Angular velocity at any instant is the derivative of the angle with respect to time. While instantaneous angular acceleration is the derivative of angular velocity with respect to time.
Examples:
- pg. 271 (Example 9-2) uses differentiation
- pg. 273 (Example 9-3) involves quadratic functions
- pg. 287 (9-2)
The tangential component of acceleration is equal to the rate of change of speed.
Examples:
- pg. 288 (9-24)
The moment of inertia is the integral of the square of the distance from the axis of rotation with respect to mass. It can also be integrates with respect to volume.
Examples:
- pg. 284 (Example 9-14) involves integration using the chain rule
- pg. 290 (9-54)
Torque utilizes the cross product which is later introduced in Calculus
Examples:
- pg. 319 (10-1)
Addition of vectors and tangents are involved in the kinetic energy of a rigid body which can be seen on pg. 302 (Figure 10-13)
Integrals are involved when dealing with work of rotational motion.
Examples:
- pg. 308 (Example 10-11)
- pg. 321 (Example 10-23)
The derivative of angular momentum equals torque.
Examples:
- pg. 311 (Example 10-12)
- pg. 322 (10-32)
