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1. Angular Quantities in Circular Motion

When a particle moves in a circular path, both the x- and y-coordinates of the particle vary with time. But since the radius of the circle remains constant, the motion can be described conveniently in terms of a single time-variant polar coordinate, . What are angular displacement, angular velocity and angular acceleration? Are angular quantities scalars or vectors? What are the relations between linear and angular quantities? What are the kinematic equations of circular motion? The video lecture “Angular Quantities in Circular Motion” answers some of these questions, and more.

2. Derivation of Centripetal Acceleration

When a particle moves in a circle with a constant speed, its velocity does not remain constant. This is because velocity is a vector and its direction along the tangent to the circle is varying continually. The corresponding acceleration of the particle is known as centripetal acceleration. We can derive the formula for centripetal acceleration by vector subtraction a method many students are not comfortable with. The video lecture “Derivation of Centripetal Acceleration” brushes up vector algebra, and then derives the said formula.

3. Two Accelerations of Non-uniform Circular Motion

4. Circular Motion with Constant Angular Acceleration

5. Problems on Circular Motion with Constant Angular Acceleration

6. Problems on Circular Motion I

7. Problems on Circular Motion II

8. Problems on Circular Motion III

9. Relation Between Linear and Angular Quantities

10. Circular Motion with Constant Angular Acceleration

11. Problems on Circular Motion with Constant Angular Acceleration

12. Examples of Uniform Circular Motion I

When a particle performs uniform circular motion, it moves at a constant speed. Since the particle possesses only centripetal acceleration, the net force acting on it is also centripetal, i.e. radially inwards towards the centre. What is a conical pendulum and what is its time period? What is the maximum speed limit of a car turning on a horizontal curve? Why do they make sloping roads at sharp turns? Does friction play a role in driver's safety? The video lecture “Uniform Circular Motion” answers some of these questions, and more.

13. Examples of Uniform Circular Motion II

14. Examples of Non-uniform Circular Motion

When a particle performs nonuniform circular motion, it moves at a varying speed. Such a particle possesses both centripetal and tangential accelerations. According to Newton's second law, the net force acting on the particle also has centripetal and tangential components. If a small ball is tied at the end of a string and revolved in a vertical circle, how does its speed vary with position? How does the tension in the string vary? Under what condition would the ball complete the circle or fly off as a projectile?The video lecture “Nonuniform Circular Motion” answers some of these questions, and more.