KINEMATICS
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Subject: Physics
Class: SHS 2
Term: 1st Term
Week: 10
Grade code: 2.1.3.LI.4
Strand code: 1
Sub-strand code: 3
Content standard code: 2.1.3.CS.1
Indicator code: 2.1.3.LI.4
Theme: MECHANICS AND MATTER
Subtheme: KINEMATICS
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This lesson focuses on a fascinating aspect of circular motion: what happens when an object is whirled in a vertical circle, like swinging a bucket of water over your head or the motion of a roller coaster loop. Unlike horizontal circular motion where gravity's effect is constant, in vertical motion, gravity either helps or opposes the tension in the string, causing the tension and speed to change throughout the path. Understanding this is crucial for engineering (designing safe amusement park rides, bridges), and it helps us see Newton's laws in action in a dynamic, real-world scenario.
Recap: Centripetal Force Before we begin, remember that any object moving in a circle at a constant speed is accelerating because its direction (and therefore velocity) is constantly changing. This acceleration is called centripetal acceleration, and it's always directed towards the centre of the circle. The force that causes this acceleration is the Centripetal Force (Fc).
The formula for centripetal force is: Fc = mv²/r where: `m` = mass of the object (kg) `v` = speed of the object (m/s) `r` = radius of the circular path (m)
The centripetal force is not a new, fundamental force. It is the *net force* pointing towards the centre of the circle. This net force can be provided by tension, gravity, friction, or a combination of forces. Motion in a Vertical Circle: The Key Idea When an object is whirled in a vertical circle, the force of gravity (its weight, W = mg) plays a crucial role. At some points, gravity helps provide the centripetal force, and at other points, it opposes the force providing it (like tension). This is why the tension in the string is not constant.
Let's analyse the forces at the two most important positions: the Top and the Bottom of the circle. Analysis at the Lowest Point (Bottom)