11 EOT Q18 Part C Page 10

Summary

In this educational video, the instructor delves into the third and final part of question 18, focusing on a car's acceleration from rest to a velocity of 22 m/s over 9 seconds with a tire diameter of 58 cm. The lesson covers the calculation of the car's angular displacement in radians, the number of tire revolutions, and the final angular speed in revolutions per second, emphasizing the importance of understanding and converting between units like radians and revolutions. The instructor uses fundamental physics equations and encourages students to practice applying these concepts.

Takeaways

• 📘 We are focusing on the last part of question number 18 from example 9.63.
• 📖 We are currently on page 10, having covered up to page 9 previously.
• 🚗 A car accelerates uniformly from rest, with initial velocity (v_i) = 0.
• 🏁 The car reaches a final speed (v_f) of 22 m/s in 9 seconds.
• 🔄 The diameter of the tire is given as 58 cm, so the radius (r) is 29 cm or 0.29 m.
• 🌀 We need to find the number of revolutions the tire makes during the car's motion.
• 🔢 The angular displacement (Theta) is calculated using the formula: Theta = 0.5 * Alpha * t^2.
• 📏 Acceleration (a) is found using the formula: a = (v_f - v_i) / t, which equals 2.44 m/s^2.
• 📐 Alpha (angular acceleration) is found using the relation: Alpha = a / r.
• 🔄 The number of revolutions is found by converting Theta from radians to revolutions using: 1 radian = 1 / (2 * pi) revolutions.
• 🔄 The final angular speed (Omega) is calculated as Omega = v / r, resulting in 75.86 rad/s or 12.07 revolutions per second.

Q & A

What is the topic of the video?

The video is about the third part or the last part of question number 18, specifically example 9.63, and it covers concepts related to a car's acceleration and the physics of its motion.

What is the initial velocity of the car mentioned in the script?

The car starts from rest, which means the initial velocity (V_i) is zero.

What is the final velocity (V_f) of the car?

The final velocity (V_f) of the car is given as 22 m/s.

What is the time taken for the car to reach the final velocity?

The time taken for the car to reach the final velocity is 9 seconds.

What is the diameter of the car's tire, and how is the radius calculated from it?

The diameter of the car's tire is given as 58 cm. The radius is calculated by dividing the diameter by 2, which gives a radius of 29 cm.

What is the formula for the number of revolutions made by the tire during the car's motion?

The number of revolutions is calculated using the formula for angular displacement (Theta), which is given by Theta = (1/2) * Alpha * t^2, where Alpha is the angular acceleration and t is time.

How is the angular acceleration (Alpha) related to the linear acceleration (a)?

The angular acceleration (Alpha) is related to the linear acceleration (a) by the formula Alpha = a / R, where R is the radius of the tire.

What is the formula used to calculate the linear acceleration (a) of the car?

The linear acceleration (a) is calculated using the formula a = (V_f - V_i) / (t_f - t_i), where V_f is the final velocity, V_i is the initial velocity, t_f is the final time, and t_i is the initial time.

How is the final angular speed (Omega) of the tire calculated?

The final angular speed (Omega) is calculated using the formula V = R * Omega, where V is the linear velocity and R is the radius of the tire.

What is the difference between the units of radian and revolution, and how do you convert between them?

A radian is a unit of angular measure, while a revolution is a complete cycle around an axis. To convert from radians to revolutions, you divide the number of radians by 2π.

What is the final angular speed of the tire in revolutions per second?

The final angular speed of the tire is calculated to be 12.07 revolutions per second.

Outlines

00:00

🚗 Introduction to the Last Part of Question 18

In this video, we will cover the third and final part of question 18, specifically example 9.63 from page 10. The focus will be on the equations and concepts necessary to solve the problem involving a car's uniform acceleration from rest to a velocity of 22 m/s over 9 seconds, with a diameter of 58 cm. Key steps include calculating the radius, converting units, and solving for the number of revolutions the tire makes.

05:04

🧮 Calculating Acceleration and Angular Displacement

We continue by calculating the acceleration of the car, which is 2.44 m/s². Using this, we find the angular displacement (Theta) by relating linear and angular quantities. The angular displacement is calculated as 341.3 radians, which is then converted to 54.33 revolutions. Detailed steps involve the use of formulas for acceleration and the relation between linear and angular variables.

10:08

🔄 Final Angular Speed and Summary

The final part of the explanation covers the calculation of the final angular speed (Omega) of the tire. By using the relation V = R * Omega, we find the angular speed to be 75.86 radians per second, which converts to 12.07 revolutions per second. Emphasis is placed on understanding the units and the formulas used. The video concludes with a reminder to practice and a preview of the next question.

Keywords

💡Acceleration

Acceleration is the rate of change of velocity of an object with respect to time. In the video, it is a key concept as the car starts from rest and accelerates uniformly to reach a certain speed. The script explains how to calculate acceleration using the formula: acceleration = (final velocity - initial velocity) / time. The example given is where the car's final velocity is 22 m/s, the initial velocity is 0 (since it starts from rest), and the time taken is 9 seconds, resulting in an acceleration of 2.44 m/s².

💡Initial Velocity

Initial velocity refers to the velocity of an object at the start of a time period or motion. In the context of the video, the car begins its motion from rest, which means its initial velocity is zero. This is an important starting point for calculating acceleration and understanding the motion dynamics of the car.

💡Final Velocity

Final velocity is the velocity of an object at the end of a time period or motion. The script mentions that the car reaches a final velocity of 22 m/s. This value is crucial for determining the acceleration and is used in the formula to calculate the change in velocity over time.

💡Time

Time is the duration over which an event occurs. In the video, the time taken for the car to accelerate and reach its final velocity is given as 9 seconds. This time value is essential in the calculation of both acceleration and the number of revolutions the tire makes.

💡Diameter

Diameter is a measure of the length of a straight line that passes through the center of a circle and connects two points on the circle's edge. The script specifies the diameter of the car's tire as 58 cm, which is then used to calculate the radius and subsequently other motion-related quantities.

💡Radius

Radius is the distance from the center of a circle to its edge. The video script explains how to find the radius from the diameter by dividing it by 2, which in this case is 29 cm. The radius is important for calculating angular displacement and other rotational quantities.

💡Revolutions

Revolutions refer to the number of complete rotations an object makes around an axis. The video discusses calculating the number of revolutions the tire makes during the car's motion, assuming no slipping occurs. This is done by converting angular displacement from radians to revolutions using the formula involving the number of revolutions and the constant pi.

💡Angular Displacement

Angular displacement, denoted by Theta in the script, is the angle through which a rotating object moves, measured in radians. The video explains how to calculate it using the formula Theta = (1/2) * acceleration * time², which is essential for determining the number of revolutions.

💡Radian

A radian is a unit of angular measurement that represents the angle at the center of a circle subtended by an arc equal in length to the radius of the circle. The video script uses radians to express angular displacement and emphasizes the importance of converting radians to revolutions for the final answer.

💡Angular Speed

Angular speed, also referred to as omega (Ω) in the script, is the rate of change of angular displacement per unit time. The video explains how to calculate the final angular speed of the tire using the relationship between linear velocity, radius, and angular speed, resulting in 12.07 revolutions per second.

💡No slipping condition

The no slipping condition implies that the car's tire rolls without slipping on the surface during its motion. This assumption is crucial for the calculations in the video, as it allows for the direct relationship between the tire's angular motion and the car's linear motion.

Highlights

Introduction to the third part of question number 18, focusing on example 9.63 from page number 10.

The car accelerates uniformly from rest, with an initial velocity of zero.

The car reaches a speed of 22 m/s in 9 seconds.

Diameter of the car's tire is given as 58 cm, leading to a radius calculation of 29 cm or 0.29 m after conversion.

Objective is to find the number of revolutions the tire makes during the car's motion, assuming no slipping occurs.

Utilizing the formula for number of revolutions, which involves calculating theta in radians and converting to revolutions.

Explanation of the relationship between linear and angular quantities: x = r * theta, v = r * omega, a = r * alpha.

Calculation of acceleration as 2.44 m/s² using the change in velocity over time.

Calculation of angular acceleration (alpha) as 2.44 / 0.29 = 8.41 rad/s².

Determination of theta as 341.3 radians, which is then converted to 5433 revolutions.

Calculation of the final angular speed (omega) using v = r * omega, resulting in 75.86 rad/s.

Conversion of angular speed to revolutions per second, resulting in approximately 12.07 revolutions per second.

Emphasis on understanding and correctly applying formulas and units, particularly the conversion between radians and revolutions.

Conclusion of the lesson on page 10, with a note to proceed to question number 19 in the next video.

Encouragement for students to practice and stay engaged with the material.

Transcripts

hello students in this video we are

going to learn about the third part or

the last part of question number 18 that

is your example

9.63 okay and this is your page number

10 it means you already finished page

till page number nine and I already

covered lots of things for you and

related to the question number 18 also

so guys in this section we are going to

check few things and I'm going to use

the equations you need to focus okay

number one a car accelerates okay

acceleration is there uniformly from

rest okay just start writing step number

one

acceleration number two starts from rest

so means initial velocity is zero and

reaches a speed okay guys just check the

unit which speed it is velocity V not

omega okay it's should be VF so third

point is VF is

22 m per second okay the fourth Point

time is given unit is seconds

fine time is your 9 second okay the

diameter okay just focus on this word h

diameter it is not given radius so

diameter is 58

cm fifth point diam

meter 58 cm first thing okay what is the

first point

radius radius is your diameter / by 2 58

cm / 2 which is equal to 29 CM clear now

the step is to convert okay so R 29 CM

which should be 29 MTI 10^ -2 M which is

equals to your

0.29 M clear guys till clear everything

okay now what is the find the number of

Revolution as I told you and guys for

solving this question you have to go

through 18. b very very very important

for you in this I'm going to use direct

the formula as we know number of

Revolution Theta

first you have to solve Theta in radian

yes or no the unit of theta is radian

then convert how to convert 1/ 2 pi

Revolution okay this thing I all already

told you number of times so Theta is

equals to Theta f is Theta

i+ Omega i t + half Alpha t² yes or no

initially at rest it means Omega I is

also zero if starts from zero it means

your Theta is also zero so Theta

f is equals to 0 + 0 + half Alpha

t² yes or no till here you understand

and the unit is radian unit is Radian

and you need to convert by dividing 1 by

2 pi okay find the number of Revolution

the tire makes during the car motion

assuming no slipping occurs okay so this

is your step number a we are looking for

number of

Revolution okay the first step we need

to find Theta which is equal to half

Alpha t² okay how to solve alp Al we

don't have the alpha okay so we know the

relation okay I'll write the relation

here as we know we have the three

relations x = r

Theta v = r Omega and third a is = to R

Alpha yes or no so can I say can I use

this relation okay so can I say a is = R

* Alpha so alpha is = to acceleration /

R radius okay now the question will come

sir where is acceleration okay

acceleration is easy now because

velocity f is given velocity I is given

and time is given so can I say use this

formula acceleration is change in

velocity V final minus V initial over

time final minus time initial okay use

this fast fast fast so a is equals to VF

Min - vi/ time what is your V

final

22 - 0 / 9 so your answer is 22 by 9 yes

or no tell me fast okay so can I say uh

what's your what is your answer 22 / 9

which is equals to acceleration is

2.44 m/s Square clear so just to solve

it can I use this equation okay let me

add a page here and then we will solve

this okay guys still here what we are

looking for Theta is equal to half Alpha

so can I say what is your alpha alpha is

your a / R okay now we solve a okay

place the value of a

22.4 2.44 sorry huh

2.44 divide by what is your time time

time time is your let's say 9 second

divide by 9 this is your Alpha so can we

solve the Theta okay I will solve Theta

here no need to use this one so Theta is

equals to your half Alpha is your 2

2.44 / 9 and t² t² is your 9 squ solve

it fast fast fast Solve IT guys so what

is your value just solve

it okay now once we solve it we get 3

41.3 and what should be the unit this is

the most important point this is the

radian and what we are looking for

number of Revolution so how to solve

radian

to radian to Revolution so I told you

you should divide by 1 / 2 pi Revolution

so solve it so theta = 3 uh

3

413

41.3 radian is equals to

3413 / 2 piun which is equals to

5433 Revolution is it fine guys radian

to Revolution clear okay now move to the

next

Point what is the final angular speed

what he's looking for he's looking for

Omega of the tire and guys this is the

most most most important thing which I'm

going to cover Revolution per second not

Revolution per minute focus on this

point huh so what we are looking for

Omega can I use this formula V = to R

Omega because we have the Velocity we

have the r we can find the Omega okay

the Maj points what you need to focus

guys Part B we are looking for V is = R

Omega Omega is = V / R till here clear

there is no doubt okay what is our

velocity okay the velocity is

22 divide by and what is your radius

just tell me

0.29 CM 0 .29 CM okay solve

this if you solve it what is your value

your value is

7586

radian per second radian per second try

to understand what is your Omega what is

the formula Theta by T Theta is your

radian and T is your time or time in

terms of second yes or

no and what he's asking you he's asking

you to convert Omega 75.86%

/ 2 pi we know radian to 1/ 2 piun

Revolution yes or no so solve this what

is your value now so your value is

12 07 Revolution per second so can I

write like this Omega isal to 75.86%

which is equals to

12.07 Revolution per second both are

same just change in the units clear guys

understand so just what he's exactly

means the questions wants to ask you

just a mixing up of the formula so you

should aware about all the formulas and

the major thing is the units you should

know the radian and the revolution how

to solve them okay guys so page number

10 is covered so I will meet you in the

question number 19 in the next video

till then take care bye and keep on

practicing okay