1. Motion in a Circle A.md
2024-4-11|2024-4-12
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Kinematics of Uniform Circular Motion
- Dictation/Definition: Define the radian and explain how angular displacement can be expressed in radians. Answer: A radian is the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle. Angular displacement in radians is the ratio of the arc length to the radius of the circle.
- Conceptual Understanding: What is angular speed, and how does it differ from linear speed? Answer: Angular speed is the rate of change of angular displacement and is a measure of how quickly an object moves around a circle. It differs from linear speed, which is the rate of change of distance. Angular speed is measured in radians per second (rad/s), while linear speed is measured in meters per second (m/s).
- Formula Recall: How do you calculate angular speed () using the period (T)? Answer: The angular speed can be calculated using the formula .
- Formula Recall: recall the formula for linear speed (v) of an object moving in a circular path in terms of its radius (r) and angular speed (). Answer: The linear speed (v) can be calculated using the formula .
Centripetal Acceleration
- Conceptual Understanding: Explain the role of centripetal acceleration in maintaining circular motion. Answer: Centripetal acceleration is the acceleration that is directed towards the center of the circle in circular motion. It is caused by a force of constant magnitude that is always perpendicular to the direction of motion. This acceleration keeps the object moving in a circular path at a constant angular speed.
- Formula Recall: How is centripetal acceleration (a) calculated using radius (r) and angular speed ()? Answer: Centripetal acceleration can be calculated using the formula .
- Alternative Formula: What is the alternative formula for calculating centripetal acceleration using linear speed (v) and radius (r)? Answer: The alternative formula for calculating centripetal acceleration is .
- Force Calculation: Derive the formula for the centripetal force (F) required to maintain circular motion in terms of mass (m), radius (r), and angular speed (). Answer: The centripetal force can be calculated using the formula .
- Alternative Force Calculation: How can you calculate the centripetal force using mass (m), linear speed (v), and radius (r)? Answer: The centripetal force can also be calculated using the formula .
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