Topicmc20d08bc3c43218e_1528449000663_0Topic

Why do bodies move in a circle?

Levelmc20d08bc3c43218e_1528449084556_0Level

Third

Core curriculummc20d08bc3c43218e_1528449076687_0Core curriculum

II. Mechanics. The student:

8) indicates the centripetal forceforceforce as the cause of uniform circular motion.

Timingmc20d08bc3c43218e_1528449068082_0Timing

45 minutes

General learning objectivesmc20d08bc3c43218e_1528449523725_0General learning objectives

Indicates the centripetal force as the cause of uniformuniformuniform circular motionmotionmotion.

Key competencesmc20d08bc3c43218e_1528449552113_0Key competences

1. Lists the properties of the centripetal forcecentripetal forcecentripetal force.

2. Applies a formula describing centripetal force.

Operational (detailed) goalsmc20d08bc3c43218e_1528450430307_0Operational (detailed) goals

The student:

- explains what uniform circular motion causes,

- determines the centripetal forceforceforce using a formula.

Methodsmc20d08bc3c43218e_1528449534267_0Methods

1. Discussion.

2. Experiment.

Forms of workmc20d08bc3c43218e_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmc20d08bc3c43218e_1528450127855_0Introduction

The students remind the basic knowledge about uniform circular motion.

What quantities describe uniform circular motion?

Proceduremc20d08bc3c43218e_1528446435040_0Procedure

The teacher asks the students to conduct simple experiment.

Task 1
Do the following simple experiment.

Experiment

Hypothesis: 
If the centripetal forcecentripetal forcecentripetal force does not act anymore, an object will change the path of its motionmotionmotion.

Materials: 
- glass (transparent mug), 
- small ball.

Instruction:
We cover the ball with a glass and move it around the circle. When the ball moves in a uniformuniformuniform motion, we raise the glass up. We observe the movement of the ball.

Observation: 
In the moment, when the glass is raised up, the ball stops to move in uniform circular motion and starts to travel along the straight line.

Explanation: 
For the body to move in a circle, the centripetal forceforceforce must act. In this case, the centripetal force is exerted on the ball by the glass’s surface. When the glass is raised up, the source of force does not exist anymore and the path of motion changes.

The teacher introduces the concept of the forces in uniform circular motion.

Centripetal forcecentripetal forceCentripetal force:
In the uniform circular motion, the direction of velocity is constantly changing, thus the acceleration vector is non‑zero. According to the first rule of dynamics to change the state of the body movement, in this case the direction of the velocity, a certain force must act on this body.

By Newton’s second law, accelerationaccelerationacceleration is linked to a force by the formula:

In uniformuniformuniform circular motion a forceforceforce is directed toward the centre of curvature of the path. This force is called the centripetal force. “Centripetal” means “centre seeking” force. This force is described by the formula:

where:
v - the velocity of an object,
r - the radius of the circle.

[Interactive graphics]

A centripetal force acts on a whirling object on a string. If the string breaks, the object will continue its motion along a tangent line.mc20d08bc3c43218e_1527752256679_0A centripetal force acts on a whirling object on a string. If the string breaks, the object will continue its motion along a tangent line.

[Illustration 1]

The students solve problems considering uniform circular motionmotionmotion.

Task 2

What centripetal forcecentripetal forcecentripetal force must act on a body moving in a circle with a constant radius if we want to double its speed? Provide some calculations to justify your answer.

Answer:

The forceforceforce must be four times greater.

Task 3

If a 150 g plastic ball is tied with a string of length 1,5 m, and it is spinning with the speed of 30 $\frac{m}{s}$, what is the centripetal force acting on it?

Answer:

F = 90 N

Centripetal force versus centrifugal forcecentrifugal forcecentrifugal force:

Centripetal forcecentripetal forceCentripetal force is directed toward the centre of a circle. This force keeps an object moving in a circular path at uniformuniformuniform speed.

Centrifugal forcecentrifugal forceCentrifugal force is an inertial forceforceforce that occurs only in non‑inertial reference frames, in this case in a frame relative to an object in circular motion.

While centripetal force is an actual force, centrifugal force is defined as an apparent force. When an object is spinning on a string, the string exerts an inward centripetal force on the mass, while mass appears to exert an outward force on the string.
Both forces can be determined using the same formula. When an object is rotating uniformly, these two forces will be equal.mc20d08bc3c43218e_1527752263647_0While centripetal force is an actual force, centrifugal force is defined as an apparent force. When an object is spinning on a string, the string exerts an inward centripetal force on the mass, while mass appears to exert an outward force on the string.
Both forces can be determined using the same formula. When an object is rotating uniformly, these two forces will be equal.

Lesson summarymc20d08bc3c43218e_1528450119332_0Lesson summary

In order to keep the body moving in a uniformuniformuniform circular motionmotionmotion, the force directed to the centre of the circle must act on it. This force is called centripetal forcecentripetal forcecentripetal force.

Selected words and expressions used in the lesson plan

centripetal forcecentripetal forcecentripetal force

centrifugal forcecentrifugal forcecentrifugal force

accelerationaccelerationacceleration

actual forceactual forceactual force

apparent forceapparent forceapparent force

forceforceforce

motionmotionmotion

uniformuniformuniform