Uniform Circular Motion?

📌 CONCEPT: Uniform circular motion is a type of motion in which an object moves in a circular path with a constant speed, but changing direction continuously.

📐 RULE / FORMULA: The centripetal force (F_c) required to maintain uniform circular motion is given by the formula F_c = (m * v^2) / r, where m is the mass of the object, v is its velocity, and r is the radius of the circular path.

💡 WORKED EXAMPLE: Given that a 5 kg particle is moving in a circular path of radius 20 m, completes one full revolution in 2 s, and has an initial speed of 2 m/s, we can calculate its final speed using the formula v = 2πr / T, where T is the time period. Then we can use the formula F_c = (m * v^2) / r to find the centripetal force required. However, the question asks for work done by an external force, which is zero since the force is applied tangentially and does no net work on the particle in one full revolution.

⚠️ COMMON MISTAKE: Students often forget that the work done by an external force on an object moving in uniform circular motion is zero when the force is applied tangentially and the object completes one full revolution.