Lesson Notes By Weeks and Term v4 - SHS 2

Lesson Video

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Performance objectives

• Explain the relationship between weight, tension, and centripetal force.
• Calculate maximum and minimum tension in a string.
• Apply these concepts to real-life scenarios.

Lesson summary

Welcome, students! Today, we are moving from describing motion (kinematics) to explaining the forces that *cause* complex motion (dynamics). Have you ever swung a bucket with some water in it over your head in a circle? Why doesn't the water fall out when the bucket is upside down? Or have you been on a Ferris wheel ('Giant Wheel') at a fair and felt heavier at the bottom and lighter at the top? These experiences are governed by the principles of vertical circular motion. Understanding these principles helps us design everything from amusement park rides to satellite orbits. It's a key concept that bridges our understanding of forces and motion.

Lesson notes

Recap: Horizontal Circular Motion Remember when we studied an object being whirled in a *horizontal* circle (like spinning a stone on a string parallel to the ground)? The speed was constant. The velocity was always changing because the direction was changing. This change in velocity (acceleration) was directed towards the centre of the circle. We called it centripetal acceleration (a_c = v²/r). The force causing this acceleration was the centripetal force (F_c = mv²/r), which was provided entirely by the tension in the string. In a horizontal circle, the weight (mg) of the object acts downwards and does not affect the tension providing the centripetal force. The Challenge: Vertical Circular Motion Now, let's consider a vertical circle. Imagine swinging a stone tied to a string in a circle that goes up and down, like a Ferris wheel.

The big difference is gravity (weight). The weight of the object (W = mg) always acts vertically downwards. At some points, weight will act *towards* the centre of the circle. At other points, it will act *away* from the centre. This means the net force towards the centre is not constant, and therefore the tension in the string must change throughout the motion.

The one thing that remains the same is the fundamental rule: The net force directed towards the centre of the circle must equal the centripetal force (mv²/r).

Let's analyse the key positions using free-body diagrams.

Evaluation guide

• Calculate maximum and minimum tension in a string.
• Talk for Learning: Discuss the relationship between the weight of a body tied to a
• string and whirled round in a vertical circle, the tension in the string and the
• centripetal force on the body