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.