About This Chapter
Calculus Applications: Circular Motion - Chapter Summary
This series of short online math lessons explores the calculus applications of circular motion. Follow along with our instructors to learn about angular velocity, rotational motion, conical pendulum equations and other related circular motion concepts. When you're finished with the chapter, you should be equipped to:
- Define angular velocity
- Understand constant angular acceleration and rotational motion
- Compare the normal and tangential components of circular motion
- Differentiate between instantaneous and uniform angular velocity of circular motion
- Solve conical pendulum equations
- Evaluate circular motion around a banked circular track
The lessons can be studied at any time of day or night, and you can ask our instructors questions whenever they arise. To help you practice solving circular motion problems on your own, we've included helpful self-assessment quizzes and a chapter exam. For your convenience, we've made the chapter accessible on any device that has an Internet connection.
1. Angular Velocity: Definition, Formula & Examples
Angular velocity applies to objects that move along a circular path. We will explore the definition of angular velocity and learn three different formulas we can use to calculate this type of velocity.
2. Rotational Motion & Constant Angular Acceleration
In this lesson, learn about the quantities used to characterize rotational motion and how to use the kinematic equations of constant acceleration motion.
3. Tangential & Normal Components of Circular Motion
Objects undergoing circular motion have two separate components: tangential and normal. In this lesson, we will derive the force equations that are tangential to the curved path and normal to the curved path.
4. Instantaneous & Uniform Angular Velocity of Circular Motion
Objects moving in a circular path have two velocities: one is an angular velocity, and the other is a tangential velocity. In this lesson, we will derive the equations for angular and tangential velocities.
5. The Conical Pendulum: Analysis & Equations
A conical pendulum is a string with a mass attached at the end. The mass moves in a horizontal circle. In this lesson, we will analyze a conical pendulum and derive equations for its angle and height.
6. Circular Motion Around a Banked Circular Track
A mass moving in a circular path on a flat surface requires friction. If that surface is banked, the mass can move in a circular path without friction, but only if the conditions are optimal. In this lesson, we will derive the equations used in banked circular motion.
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Other chapters within the HSC Mathematics: Exam Prep & Syllabus course
- Mathematical Proofs & Reasoning
- Basic Arithmetic & Algebra
- Factorization of Binomials & Trinomials
- Types of Equations & Inequalities
- Plane Geometry
- Circle Plane Geometry
- Probability & Randomization
- Arithmetic & Geometric Series
- Trigonometric Ratios
- Geometrical Representations of Functions
- Linear Functions & Lines
- Derivatives of Functions
- Quadratic Polynomials & Parabolas
- Geometrical Applications of Differentiation
- Logarithmic & Exponential Functions
- Calculating Trigonometric Functions
- Understanding Inverse Functions
- Factoring & Graphing Polynomials
- Roots & Coefficients of Polynomials
- Binomial Theorem & Probability
- Graphing & Solving Functions
- Solving & Graphing Complex Numbers
- Geometric Representations of Complex Numbers
- Square Roots, Powers & Roots of Complex Numbers
- Conic Sections Basics
- The Ellipse in Algebra
- The Hyperbola
- The Rectangular Hyperbola
- Calculus Applications: Rate of Change
- Calculus Applications: Velocity & Acceleration
- Calculus Applications: Projectile & Harmonic Motion
- Calculus Applications: Resisted Motion
- HSC Mathematics Flashcards