LESSON PLAN”Circular Motion”

Educational Unit : Senior High Shcool

Subject : Physics

Class / Term : X/ 1

Time allocation : 2 x 45 minutes

I. STANDARD OF COMPETENCE

2. To apply basic concept and principle of kinematic and dynamic point

matter

II. BASIC COMPETENCE

II.2To analyze physics quantities at circular motion with constant velocity.

III. INDICATOR

A. Kognitif

1. Product

To mention physics quantities of angular motion with constant

velocity

To explain The definition of angular motion

To explain about frequency and period

To explain about angular displacement

To explain about angular velocity

To connect angular quantities with tangensial quantities

2. Proccess

Do the experiment to determine angular velocity and centripental force,

consist of:

Formulating problem

Formulating hypotesis

Data Collecting

Data Proccessing

Conclude

B. Psycomotor

To measure the time to do circular motion with some different

radius

To determine angular velocity and centripental force

C. Affective

Character: Think creative, work accurately, honest, responsible

Social skill: share the idea, be a good listener and answer idea from the

other

IV. OBJECTIVES

A. Kognitif

1. Product

With their opinion, the students can mention physics quantities of

angular motion with constant velocity

With their opinion, the students can explain The definition of

angular motion

With their opinion, the students can explain about frequency and

period

With their opinion, the students can explain about angular

displacement

With their opinion, the students can explain about angular velocity

With their opinion, the students can connect angular quantities with

tangensial quantities

3. Proccess

Provided a set equipment of circular motion experimental,

student can do observation to determine angular velocity and

centripental force according to details of task which is determined at

worksheet: Formulating problem, Formulating hypothesis, , data

collecting, communicate the data, analyze the data, Conclude.

2. Psycomotor

Provided a set equipment of circular motion experimental, student can

measure the time to do circular motion with some different radius

Provided a set equipment of circular motion experimental, student can

determine angular velocity and centripental force

3. Affective

Active in the learning activity dan show the character think creative,

work accurately, honest, responsible.

Colaborate in the hands on activity, share the idea, be a good listener

and answer idea from the other actively.

V. LEARNING MATERIALS

What is circular motion? A matter moves with circle strip (full or

partly) is called circular motion. Circular motion is the motion with circle

strip (full or partly). A matter is called move in circular motion because the

strip is circle. There are many kinds of application include circular motion in

daily life.

Each matter that move in circular motion must be move in rotate

motion with sufe of rotation in the form of straight line that through center of

circle strip. On the contrary a matter that move in rotate motion not exactly

move in circular motion.

T is period of rotation, that is time which is needed to once of rotation,

and the formula is

T=1f

ω is angle’s velocity, that is a large of angle which is wiped by radius

each time.

v=ωRω=2 π

T

The formula of sentripetal acceleration

a s=ω2R= v2

R

VI. LEARNING MODEL

- Model : Consept

- Method : discussion, experiment.

VII.TEACHING LEARNING PROCESS

1) Introduction (10 minutes)

Convey learning objective.

Prepare students to learn by explaining little concept about circular

motion.

2) Main Activity (65 minutes)

Show Sample and Non-Sample

Teacher shows sample of circular motion to students, for example:

An ant sticks at fan which rotate on roof.

A grain of sand rushes by wheel of cart.

Show non-sample of circular motion.

Shot off projectille motion

Explain little concept of angle’s velocity and angle’s acceleration.

Analyze Hypothesis

Teacher and students make hypothesis about the topic.

Give worksheet to students.

Analyze hypothesis by doing experiment to determine angle’s velocity

and angle’s acceleration.

Check Concept and Give Feedback

Give feedback to students by asking about conclusion in experiment.

Check concept that has received by students.

3) Closure (15 minutes)

Closure

Guide students to conclude the topic.

Give chance to ask if there is miss conception.

Application

Ask students to mention some samples about circular motion in daily

life.

Teacher gives evaluation.

A. ASSESMENT Writing test Activity test

B. TEACHING RESOURCES Hand Out Worksheet

C. EQUIPMENT Stopwatch Rule Glass tube 2 hole rubber stopper Light cord Load

Figure 3.2. point P rotate with O ordinat

An object moves in a straight line if its total force works on the object direction, or equal zero. If the total force works by forms an angle to moving direction in every time, The object will move on the curve path. For example wheel motion and ball motion in the circular string tip.

A. Definition of uniform circular motion

uniform circular motion is motion with circular path and constant speed and velocity direction is perpendicular by acceleration direction. The velocity direction always changes but the object move in this circle. It has shown in figure 3.1. Because of the acceleration defined as velocity changing. Velocity direction and velocity value changing cause acceleration. So, the object that move around the circle accelerates continually, even when the speed is constant (v1=v2= v)

B. Quantities in the circular motion1. Period and frequency

An object that moves around, its motion will always repeat periodically. By see a point on the motion path, a particle that has done one full circle will back or trought the first position. Circular motion describe in the frequency (f), it is total rotation in every time quantities or total rotation per second and period (T) is needed time to reach one rotation.

Relationship between period (T) and frequency (f) is:

T=1f

or f =1T

………………………..(3.1)

With, T = period (s); f = frequency (Hz)The example is if an object moves around with frequency 3

rotation/s, so fr do 1 full rotation, the object need time 1/3 second. For the object that around forming circle with constant speed v, can written:

v=2 πRT

………………………………..(3.2)

It caused in one rotation, this object sail trought one circle around.2. Angular position θ

Figure 3.2 draw a point P that around to ordinat That perpendicular with pictured area trought point O. point P move from A to B in time t. P position can be shown from angular value that reached, it is θ that formed by AB to x ordinat that trought O. angular

Figure 3.1. an object move around like circle

Figure 3.3. point P rotate with fixed ordinat O and radii R

Figure 3.4. angular velocity perpendicular with circle

position θ is given radian unit. Angular value of one rotation is 3600=2θ radian.

If θ is angle of center circle that has length bow s and radii R, gotten relationship:

θ= sR

…………………….(3.3)

With, θ = angular position (rad); s = bow path (m); R = radii (m)3. Angular velocity

In the uniform circular motion, Angular velocity for the same times is always constant. Angular velocity defined as total angle in every one time unit. For the particle that do once rotation, was got reached angle θ =

2π and time reached t = T. So that, angular velocity (𝝎) in uniform circular motion can be formulated:

ω=2 πT

or ω=2 πf ……………………….(3.4)

With: 𝝎 is angular velocity (rad/s); T is period (s); f is frequency (Hz)

C. Relationship between angular quantities and tangensial quantities1. Angular position θ and legth path s

Figure 3.3 show that point P move circular with fixed ordinat O and radii R. if P moves from A to B by reach bow path s, and the made angular position is θ, so we find relation:

θ= sR

………………(3.5)

With, θ is path or angular position (rad); s is path of bow (m); R is radii (m).2. Angular velocity 𝝎 And linear velocity

If angular position is very small, or Δθ, because the time (Δt) is very small, the path of bow is also very small too, or Δs, so that equation 3.5 changed be:

∆ s=∆ θ . RIf its equation devided by time needed Δt,

we find: ∆ s∆ t

=∆ θ .R∆ t

If Δs small so its equation be:dsdt

=dθ . Rdt

v=ω. R………………(3.6)

With: v is linear velocity (m/s); 𝝎 is angular velocity (rad/s) and R is radii of path (m)

Linear velocity has direction as whorled tangent direction on its

points, one of it is point P. in other hand, angular velocity 𝝎 has onto direction, perpendicular by circle surface, like the figure 3.4.3. Centripental acceleration

Acceleration that always direct into center circle is named centripental acceleration (ac). it is formulated by:

Figure 3.5. determine velocity changing in the uniform circular

as=v2−v1

∆ t=∆ v

∆ t

With, Δv is velocity changing in short time Δt. Finally, we will regard situation where Δt approaching 0, so that we will find momentary acceleration. In the figure 3.5(a), in time Δt, the particle move from point A to point B with reach the distance Δl researching bow that makes angle Δθ. Vector velocity changing is

v2−v1=∆ v, that show in the figure 3.5 (b). if we

determine Δt very small (approaching 0), so Δl and Δθ also very small and v2 nearly parallel with v1, and Δv will perpendicular to the both. Thus, Δv towards the

center circle. Because as has a same direction with Δv, a has to direct to the center circle. Thus, this acceleration called centripental acceleration (acceleration that look for the center) or radial acceleration (because it has direction

along radii, into circle center), and given notation as.How to determine the centripental acceleration? Because of CA

perpendicular with v2, Δθ define as the angle between CA and CB, it also the angle between v1 and v2. Thus, v2, v1 and Δv showed by figure 3.5(b), shape the same geometrically triangle with ABC triangle in the figure 3.5(a). By use small Δθ (and use very small Δt) can written:

∆ vv

= NR

We have determined that v=v1=v2, because we assume that velocity is constant. This equation is right if Δt approaching zero, because it will make Δl = AB browstring. To find momentary acceleration, with Δt approaching zero, we write equation above:

∆ v= vR

∆l

To find centripental acceleration, we devide Δv by Δt:

as=∆ v∆ R

= vR

∆ l∆ t

And because ∆ l∆ t

is linear speed ‘v’ from its object, so:

as=v2

R…………………….(3.7)

With:as is centripental acceleration (m/s2)v is linear velocity (m/s)R is radii of path (m)

Figure 3.6.for uniform circular motion,a always perpendicular

Based on eq(3.7), we can conclude that centripental acceleration depend on v and R. if speed v is faster, so direction velocity changing is faster too. And if radii R is bigger, direction velocity changing is slower.

Acceleration vector is toward into center circle, but velocity vector always toward into tangential motion of circle. Thus, velocity vector and acceleration are perpendicular with others for every point on its path for uniform circular motion, as shown at the figure 3.8.

a) Basic Competence:

2.2 To analyze physics quantity at circular motion with constant velocity.

b) Objective:

Do experiment to determine relationship between centripental force

and angular velocity

c) Apparatus and Material:

1. Stopwatch

2. Glass tube

3. 2 hole rubber stopper

4. Light cord

5. Load

d) Procedure:

1. Find the mass of the

loads which are

hanging at the end of

the string, and the mass of the stopper.

2. Have one lab group member carefully swing the stopper on the string

in a horizontal circle above his or her head.

3. When the radius is constant (that is, the loads are not moving up or

down), and the period of rotation is consistent, have another lab group

member find the time for 10 revolutions.

4. At the end of 10 revolutions, put your finger on the end of the tube to

preserve the radius at which the stopper on the end of the string was

rotating.

5. Measure the radius of the circle (the length of the string).

6. Find the period, and then using the period and the radius, find the

velocity of the stopper as it rotates.

7. Using the mass, velocity, and radius, calculate the centripetal force

acting on the stopper. Should you use the mass of the stopper or the

mass of the loads in the equation for centripetal force?

8. Compare the value you measured for the centripetal force with the

weight (not the mass) of the loads.

9. Repeat steps b through g for a different radius.

10. Record all relevant data in the table below, and answer the questions

on the back of this sheet.

f) Table:

Exp. No m (kg) R (rad) t (s) 𝝎(rad/s)=10/t v (m/s) Fc

1.

2.

3.

4.

5.

g) Discuss:

1. Create a graphic centripental force vs angular velocity!

h) Conclusion:

........................................................................................................................

........................................................................................................................

........................................................................................................................

Fc (N)

𝝎 (rad/s)

1. What is circular motion?

2. Mention some samples of circular motion in daily life!

3. How is the connection between circular motion and rotate motion?

4. Our solar system is situated about 3,086 x 1020 m from center of galaxy and

around it 250 km/s. From each measurement and calculation knowing that our

solar system born about 6 billion years ago. How many times our solar system

has arounded the center of galaxy?

5. From evaluation number 4, calculate sentripetal acceleration our solar system

around the center of galaxy!

1. Circular motion is the motion with circle strip (full or partly). A matter is called move in circular motion because the strip is circle.

2. Some samples of circular motion in daily life:

Vehicles rush by circle of Indonesian Hotel.

An ant sticks at fan which rotate on roof.

A grain of sand rushes by wheel of cart.

When we through the road along high lands that winding.

Motion of moving bor.

Spin a top.

Etc.

3. Each matter that move in circular motion must be move in rotate motion

with sufe of rotation in the form of straight line that through center of circle

strip. On the contrary a matter that move in rotate motion not exactly move

in circular motion.

4. If our solar system around the center of galaxy may be considered as circular

motion, circle radius of the strip is 3,086 x 1020 m. The linear velocity of our

solar system is 250 km/s or 2,5 x 105 m/s. So,

ω= vR

= 2,5 x105 m /s3 , 086 x 1020m

=8 , 101 x10−16 rad /s

The period is

T=2 πω

=7 , 756 x1017 s

5. Circle radius of solar system strip is 3,086 x 1020m and linear velocity is 2,5

x 105 m/s, so sentripetal acceleration of our solar system is

as=( 2,5 x 105 m / s)2

3 ,086 x 1020 m=2 ,025 x 10−10m / s2

Rosyid, Muhammad Farchani. 2008. Kajian Konsep Fisika 1. Solo: Tiga

Serangkai

Sumarsono, Joko. 2009. Fisika: Untuk SMA/MA Kelas X. Jakarta: Pusat

Perbukuan, Departemen Pendidikan Nasional,

Handayani, Sri. 2009. Fisika 1 : Untuk SMA/MA Kelas X. Jakarta: Pusat

Perbukuan, Departemen Pendidikan Nasional,

PSICOMOTOR ASSESMENT SHEET

Assesment Item

- Do experiment about centripental forca and angular velocity in the circular

motion

- Explain the concept to be real appliede

Guide :

Give check ( ) in the column for aspect that suitable with perception data

No Aspect Do Score NoteYes No 4 3 2 1

Teaching Learning Activity1 Do experiment 2 Present the result of each

experiment3 Explain the circular motion

that happened 4 Make conclusion about the

relationship between centripental forcé and angular velocity

5 Give example of application of circular motion in daily life

Final Score

Psicomotor Asessment Rubric

No Aspec Rubric NoteTeaching Learning Activity 1 Do experiment 4. Correctly, suitable with procedure and

complete equipment 3. Suitable with precedure, but not

complete equipment2. Not suitable with procedure , but

complete equipment 1. Not suitable with procedure , and not

complete equipment 2 Presentate result of

each experiment4. Right result, and with media3. Right result, without media2. Wrong result, with media1. Wrong result, without media

3 Explain the circular motion that happened

4. Very complete3. Complete2. Complete enough1. Less complete

4 Make conclusion about the relationship between centripental forcé and angular velocity

4. Right result, and very complete3. Right result, and complete enough2. Right result, and not complete1. Wrong result

5 Give example of application of circular

4. Right result, and very complete3. Right result, and complete enough

motion in daily life 2. Right result, and not complete1. Wrong result

Final Score

AFECTIVE ASSESMENT SHEET

Guide :

This sheet will use after teaching learning activity begin.

Give check ( ) in the column for aspec that suitable with perception data

No Aspec Do Score NoteYes No 4 3 2 1

1 Attendance student2 Preparation3 Participate in activity5 Cooperation in group6 Presentate result7 Discuss activity

Jumlah Skor

AFEKTIF ASSESMEN RUBRICNo Aspec Rubric Note1 Attendance student 4. On time

3. Late less 15 minutes2. Late over 15 minutes1. No attend

2 Preparation 4. Complete3. Complete enough2. Less complete1. Not complete

3 Participate in activity 4. Very active3. Active2. Less Active1. Not active

4 Cooperation in group 4. Very active3. Active2. Less Active1. Not active

6 Presentate result 4. Presentate in front of class3. Active to answer question2. Active to help answer question1. Not active

7 Discuss activity 4. Very active3. Active2. Less Active1. Not active

Score

PHYSICS

SENIOR HIGH SHCOOL10th CLASS

Standard of Competence:

2. To apply basic concept and principle of kinematic and dynamic point

matter.

Basic Competence :

2.2 To analyze physics quantity at circular motion with constant velocity.

Created by:Alfi Nurlailiyah(083184012)

PHYSICS DEPARTMENTMATHEMATIC AND SCIENCE FACULTY

SURABAYA STATE UNIVERSITY2011