11 EOT Q18 Part C Page 10
Summary
TLDRIn 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
🚗 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.
🧮 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.
🔄 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.
Mindmap
Keywords
💡Acceleration
💡Initial Velocity
💡Final Velocity
💡Time
💡Diameter
💡Radius
💡Revolutions
💡Angular Displacement
💡Radian
💡Angular Speed
💡No slipping condition
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
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