View source for Apps-On-Physics/C2/Circular-motion/English

{|border=1
|-
|| '''Visual Cue'''
|| '''Narration'''
|-
|| '''Slide Number 1 '''

'''Title Slide'''
|| Welcome to this tutorial on '''Circular Motion.'''
|-
|| '''Slide Number 2 '''

'''Learning objective '''
|| In this tutorial we will demonstrate,

*'''Uniform Circular Motion''' and 
*'''Model of a Carousel Apps.'''
|-
|| '''Slide Number 3'''

'''System Requirements'''
|| Here I am using,

*Ubuntu Linux OS version 16.04
*Firefox web browser version 62.0.3

|-
|| '''Slide Number 4'''

'''Pre-requities'''

'''https://spoken-tutorial.org'''
|| To follow this tutorial learner should be familiar with '''Apps on Physics'''.

For the pre-requisite tutorials please visit this site.

|-
|| '''Slide Number 5'''

'''Learning Goals'''
|| Using these '''Apps''' we will, 


* Show the change in position, velocity, acceleration and force with time.
* Calculate angular velocity and angular acceleration.
* Demonstrate the motion of a carousel.
* Calculate centripetal force.

|-
|| '''Slide Number 6'''

'''Uniform Circular Motion'''

It is a motion of an object on a circular path with a constant speed.

Example: Moon, revolves around the earth in uniform circular motion.

|| Let us first define uniform circular motion.

It is a motion of an object on a circular path with a constant speed.

For example: Moon, revolves around the earth in uniform circular motion.

|-
|| '''Slide Number 7'''

'''Link for Apps on physics. '''

'''https://www.walter-fendt.de/html5/phen/'''
|| Use the given link to download the '''Apps on Physics'''.

'''https://www.walter-fendt.de/html5/phen/'''
|-
|| Open the '''Downloads '''folder.
|| I have already downloaded the '''Apps on Physics''' to my '''Downloads''' folder.

|-
|| Right click on '''circularmotion_en.htm''' file.

Select the option '''Open With Firefox web Browser''' option.

Cursor on the '''App'''.

|| Right-click on '''circularmotion_en.htm''' file.

Select the option '''Open With Firefox Web Browser'''.

'''Uniform Circular Motion app''' opens in the '''browser'''.

|-
|| Point to the white point.
|| The interface shows a white coloured point on a circular path. 

This white coloured point behaves as an object on a circular path.

|-
|| Scroll down to see the '''App''' completely.
|| Scroll down to see the complete interface.

|-
|| Point to the graph.
|| Next to the circular path, we see a graph.

This graph shows the change in position of the object with time.

|-
|| Click on the '''Start''' button in the green control panel.
|| Click on the '''Start''' button.

|-
|| Click on the '''Slow motion''' check-box.
|| Click on the '''Slow motion''' check-box to see the motion steadily.

|-
|| Point to bold red vector and then the other two vectors on '''x''' and '''y''' axis.
|| The bold red vector shows the instantaneous position of the point. 

The other two red vectors show the position of the point along the '''x''' and '''y''' axis.

|-
|| Click on '''Slow motion''' check-box.
|| Uncheck the '''Slow motion''' check-box.

|-
|| Click on the '''Reset''' button.
|| Click on the '''Reset''' button to reset the '''App'''.
|-
|| Point to the red dots on the graph.
|| The initial position of the white point is 2 '''metre''' on '''x'''-axis and 0 '''metre''' on '''y'''-axis.

|-
|| Point to the red vector.
|| This is because the white point is on the circle that has a radius of 2 '''metre'''.

And it is pointing in the positive x-axis.

|-
|| Point to the radio button.
Click on the '''Velocity''' radio button.
 
|| Click on the '''Velocity''' radio button.

|-
|| Point to the pink vector.
|| Observe that the direction of the velocity vector is tangential to the circular path.

|-
|| Click on '''Start''' button.
|| Click on the '''Start''' button and observe the change in direction of velocity.

|-
|| Point to the velocity vector.
|| Notice that the magnitude of the velocity is same but its direction changes continuously.

|-
|| Point to the '''y'''-axis.
|| Observe that the representation on the y-axis has changed to velocity.

|-
|| Point to the name of '''y'''-axis.
|| In the graph y-axis has changed from x, y to V<sub>x </sub>, V<sub>y</sub>.

|-
|| Click on the '''Reset''' button.
|| Click on the '''Reset''' button.

|-
|| Point to angular velocity.

Point to the value
|| Above the linear velocity the '''App''' has shown '''Angular velocity''', denoted by '''omega'''.

The value of '''omega''' is 1.26 '''radians per second'''.

|-
|| Click on the '''Start''' button.
|| Click on the '''Start''' button.

|-
|| Select '''Slow motion''' check-box.
|| Select '''Slow motion''' check-box.

|-
|| Point to the bold Pink colour vector
|| Here the bold pink vector shows the magnitude and direction of velocity.

|-
|| Point to other faint '''x''' and '''y''' coordinates.
|| The other two vectors show the magnitude and direction on the '''x''' and '''y''' coordinates.

|-
|| Uncheck the '''Slow motion''' check-box.
|| Uncheck the '''Slow motion''' check box.

|-
|| Make a png for the formula and display on the interface.

'''ω=v/r '''

ω = angular velocity 

v= linear velocity

r = radius
|| We can calculate angular velocity using the formula.

'''ω=v/r'''

where '''ω '''is angular velocity 

'''v '''is linear velocity and

'''r '''is radius of the circle

|-
|| Click on the '''Reset''' button.
|| Click on the '''Reset''' button.

|-
||Press '''Enter''' after changing every value.

Change '''Radius''' to 5 '''metre''', '''Period '''to 10 '''s'''and '''Mass''' to 10 '''Kg'''.
|| Change the '''Radius''' to 5 '''metre,'''

'''Period''' to 10 '''seconds''' and '''Mass''' of the object to 10 '''kg'''.

Press '''Enter''' after changing every value.

|-
|| Show a png 

ω=v/r

<nowiki>=3.14/ 5</nowiki>

<nowiki>= 0.628 rad/s</nowiki>
|| I have already calculated the value of angular velocity.

|- 
|| Point to the value.
|| The value of angular velocity is 0.628 '''rad/s (radians per second)'''.

|-
|| Point to the measured value of '''Angular velocity''' by the '''App'''.
|| The calculated value is same as the value shown in the '''App'''.

|-
|| Click on '''Acceleration''' radio button.
|| Click on the '''Acceleration''' radio button.

|-
|| Point to blue vector as centripetal acceleration.
|| Here the blue vector shows the direction of acceleration.

This acceleration is centripetal acceleration.

|-
|| Point to '''a=1.97 m/s<sup>2'''</sup>.
|| The magnitude of acceleration is 1.97 '''metre per second square'''. 

|-
|| Point to the blue arrow.
|| The direction of acceleration is towards the center of the circle.

|-
|| Make a png to show the formula on the interface. ['''a<sub>c</sub><nowiki>=</nowiki>ω<sup>2</sup>r]'''

Click on '''Velocity '''radio button.
|| This is the formula to calculate centripetal acceleration.

Click on '''Velocity''' radio button.

|-
|| Show the angular velocity value and radius.
|| Substitute the values of angular velocity and radius into the formula.

|-
|| Click on '''Acceleration''' radio button.

'''Show a png'''

'''a<sub>c</sub><nowiki>=</nowiki>ω<sup>2</sup>r'''

'''<nowiki>=(0.628)</nowiki><sup>2 </sup>x 5'''

'''<nowiki>=1.97 m/s</nowiki><sup>2'''</sup>
|| Again click on '''Acceleration''' radio button.

Here is the calculated value of centripetal acceleration.

Observe that the calculated value is same as the one shown in the '''App'''.

|-
|| Click''' Force''' radio button.
|| Click on the '''Force''' radio button.

|-
|| Point to the '''Force''' vector.
|| Note that the direction of '''Force''' vector is same as that of the '''Acceleration''' vector.

|-
|| F directly proportional to acceleration.
|| Recall from '''Newton's''' second law that force and acceleration are directly related to each other.

|-
||Click on the '''Start''' button.
||Click on the '''Start''' button.

|-
|| Point to the force vector.
|| Force acting on a circular field is a centripetal force.

|-
|| Point to the vector that is directed towards the center.
|| This force is always directed towards the center.

|-
||Click on the '''Reset''' button.
||Click on the '''Reset''' button.

|-
|| '''Slide Number 8'''

'''Numerical'''

Consider the white point as a toy car of mass 1 Kg that moves 

on a circular track of radius 5.00 m in 10.0 seconds. 

Calculate the centripetal acceleration of the car.

|| Let us solve a numerical to find centripetal acceleration.

Please pause the video and read the numerical.

|-
|| Edit the values of '''Radius''' to 8 '''m''' and '''Period''' to 10 '''sec'''.
|| Then change the parameters according to the numerical.

|-
|| Cursor on the interface.
|| Details about all calculations are shown in the additional material.

|-
|| Cursor on the interface.
|| For now I will calculate centripetal acceleration using the formula.

|-
|| Click on '''Velocity''' radio button.
|| Click on '''Velocity''' radio button.

|-
|| Make a text-box to show the calculation.

a<sub>c</sub><nowiki>=</nowiki>ω<sup>2</sup>r

<nowiki>= (0.628 )</nowiki><sup>2</sup> x 8

<nowiki>= 3.15 m/s</nowiki><sup>2 </sup>
|| Let us substitute the values of angular velocity and radius into the formula.

The calculated value of centripetal acceleration is 3.15 '''metre per second square'''.

|-
|| Click on''' Acceleration''' radio button.
|| Click on the '''Acceleration''' radio button to compare the value.

|-
|| Point to the value of '''Acceleration'''.
|| Observe that the values are comparable.

|-
|| '''Slide Number 9'''

'''Assignment'''

A particle of mass 0.2 kg moves on a circle of radius 2 m in a time period of 10 s.

Find the angular velocity.
|| As an assignment solve the following numericals by changing the parameters.

|-
|| '''Slide Number 10'''

'''Assignment'''

A toy car of mass 2 Kg moves on a circle of radius 10 m. 

In a time period of 10 s. Find the values of angular velocity and centripetal force.
|| 

|-
|| 
|| Let us move on to '''Carousel App'''.

|-
|| '''html5phen'''<< '''phen'''<<'''carousel_en.htm '''

<<right click on the file name<< open with firefox web browser. 
|| To open the '''App''' right-click on '''carousel_en.htm''' file and '''Open With Firefox Web Browser'''.

|-
|| Cursor on the interface.
|| '''Model of a Carousel App''' opens in the '''browser'''.

Below the name a short description about the interface is given.

|-
|| Scroll down to see the interface.
|| Let us scroll down to see the interface.

|-
|| Cursor on the interface.
|| This '''App''' shows the application of centripetal force.

|-
|| Point to the attached pendulums.
|| Notice that eight pendulums are attached to the carousel.

|-
|| Point to''' Carousel''' radio button. 
|| Here we have four radio buttons.

By default '''Carousel '''is selected.

|-
|| Make a box while editing and Point to the text-fields.
|| In the green panel we can change the values of the text-fields.

|-
|| Edit the value for '''Period''' as 2. 

point to the movement of the carousel.
|| Let us change the '''Period''' to 2 seconds and press '''Enter'''.

Notice that the speed of the carousel has increased.

Due to increase in speed radius of the axis of rotation increases.

|-
|| Point to the pendulums.
|| The pendulums move away from the center.

|-
|| Click on the '''Numerical values''' radio button.
|| Click on the '''Numerical values''' radio button.

|-
|| Point to the values.
|| Here we can see different parameters that '''App''' has calculated.

|-
|| Point to the value of '''Velocity'''.
|| The value of '''Velocity''' is 5.21 '''metre per second'''. 

|-
|| Point the values of '''Frequency''', '''Angular velocity''', and '''Centripetal force'''.
|| Note the values of '''Frequency''', '''Angular velocity''', and '''Centripetal force'''.

|-
|| Change '''Period''' to 5 seconds.
|| Let us increase the '''Period''' to 5 seconds.

|-
|| Point to the '''Frequency''', '''Angular velocity''', and '''Centripetal force'''.
|| As we increase the '''Period''', '''Frequency''', '''Angular velocity ''' 

and '''Centripetal force''' have decreased.

|-
|| Click on the '''Carousel''' radio button.
|| Click on the '''Carousel''' radio button.

|-
|| Point to the carousel.
|| Observe that the carousel speed has slowed down.

|-
|| Change '''Distance between suspensions and axis of rotation''' to 1 '''metre'''.
|| Let’s change '''Distance between suspensions and axis of rotation''' to 1 '''metre'''.

|-
|| Point to '''Distance between suspensions and axis of rotation'''.
|| '''Distance between suspensions and axis of rotation''' can be changed from 0 to 1 '''metre'''.

|-
|| Point to the carousel.
|| Observe that the size of the carousel has increased.

|-
|| Change the '''Distance between suspensions and axis of rotation''' to 0.3 '''metre'''.
|| Let’s decrease '''Distance between suspensions and axis of rotation''' to 0.3 '''metre'''.

|-
|| Point to the carousel.
|| Note the decrease in the size of the carousel.

|-
|| Point to the '''Length of the string'''.
|| Change the '''Length of the string''' to 0.5 '''metre''' and observe the changes on the carousel.

|-
|| Point to the '''Length of the string'''.
|| Note that we can vary the '''Length of the string''' between 0 to 1 metre.

|-
|| Change the '''Mass''' to 0.1 '''kg'''  and then to 10 '''kg'''  to show the change.
|| Similarly we can vary the '''Mass''' between 0.1 to 10 '''kg'''.

|-
|| Click on '''F5''' key on the keyboard to''' Reset'''.
|| Click on '''F5''' key on the keyboard to '''Reset''' the '''App'''.

|-
|| Click on '''Carousel with forces''' radio button.
|| Click on the '''Carousel with forces''' radio button.

|-
|| Point to the vectors.
|| Here it shows three force vectors.

|-
|| Change the value of '''Period''' to 2 '''seconds''' .
|| Let us change '''Period''' to 2 '''seconds'''  to see the vectors clearly.

|-
|| Click on the '''Pause''' button.
|| Click on the '''Pause''' button.

|-
|| Point to black vector.

Point to blue vector.

Point to red vector.

|| Black vector shows the force due to the weight.

Blue vector shows the force exerted by the string 

And red vector is the net force pointing inward.

|-
|| Select '''Sketch''' radio button.
|| To get a clear view of the vectors let us select '''Sketch''' radio button. 

|-
|| Point to the interface.
|| Here we can see a 2D view of the force vectors.

|-
|| Click on '''Carousel''' radio button. 
|| Click on '''Carousel''' radio button. 

|-
|| Click on the '''Resume''' button.
|| Click on the '''Resume''' button.

|-
|| '''Slide Number 11'''

'''Numerical'''

The toy horse suspended to a carousel has a mass of 1.5 kg. 

It moves on a circular base with a period of 4 s. 

If its distance between the suspension and axis of rotation is 1 m, calculate centripetal force.

|| Let us solve a numerical by varying the parameters in the '''App'''.

Please pause the video and read the numerical.
|-
|| Change and point to show the values.
|| Let us change the values according to the numerical.

|-
|| Make png to show the formula on the interface.

'''F<sub>c</sub><nowiki>= mv</nowiki><sup>2</sup>/r'''
|| To calculate the centripetal force we can use the formula :

'''F<sub>c</sub><nowiki>= mv</nowiki><sup>2</sup>/r'''

|-
|| Click on '''Numerical values''' radio button.
|| Click on the '''Numerical values''' radio button.

|-
|| Point to show the value of radius and velocity.
|| From here we will take the values of radius and velocity.

|-
|| 
|| Now calculate the value of centripetal force. 

|-
|| '''Show it on a text-box'''.

'''F<sub>c</sub><nowiki>= mv</nowiki><sup>2</sup>/r'''

'''<nowiki>= </nowiki><u>1.5 x 2.06 x 2.06'''</u>

'''1.31'''

'''<nowiki>= </nowiki>4.85 N'''
|| Substitute the values into the formula.

We get the value of centripetal force as 4.85 '''Newton'''.

|-
|| Point to the values side by side.
|| Observe that the values are comparable.

|-
|| '''Slide Number 12'''

'''Assignment'''

The toy horse suspended to a carousel has a mass of 5 kg,

it moves on a circular base with a period of 3 s.
 
If its distance between the suspension and axis of rotation is 0.5 m,

calculate angular velocity, angular acceleration and centripetal force.
|| As an assignment solve the given numerical.

|-
|| 
|| Let us summarise

|-
|| '''Slide Number 13'''

'''Summary'''
|| Using these '''Apps''' we have,
 
* Shown the change in position, velocity, acceleration and force with time.

* Calculated angular velocity and angular acceleration.

* Demonstrated the motion of a carousel.

* Calculated centripetal force.

|-
|| '''Slide Number 14'''

'''Acknowledgement'''

These Apps were created by Walter-fendt and his team.
|| These '''Apps''' were created by '''Walter-fendt''' and his team.

|-
|| '''Slide Number 15'''

'''About Spoken Tutorial project'''.

|| The video at the following link summarizes the Spoken Tutorial project.

Please download and watch it.

|-
|| '''Slide Number 16'''

'''Spoken Tutorial workshops'''.

|| The&nbsp;'''Spoken Tutorial Project&nbsp;'''team,

conducts workshops and gives certificates.

For more information, please write to us.

|-
|| '''Slide Number 17'''

'''Forum for specific questions:'''

Do you have questions in THIS Spoken Tutorial?

Please visit this site

Choose the minute and second where you have the question. 

Explain your question briefly.

Someone from our team will answer them.
|| Please post your timed queries on this forum.
|-
|| '''Slide Number 18'''

'''Acknowledgement'''
|| Spoken Tutorial Project is funded by MHRD Government of India.

|-
|| 
|| This is Himanshi Karwanje from IIT-Bombay. 

Thank you for joining.
|-
|}