Calculating Linear and Angular Velocity with Distance and Time

TLDR; Calculating linear and angular velocity using distance, time, and central angle. Examples include runner's average velocity, angular velocity of a mechanical arm, and linear velocity around a circle.

⭐ Introduction

The video aims to calculate linear and angular velocity using distance and time.

Linear velocity is measured on pulleys or disks, while angular velocity measures the change in central angles.

The fundamental formula for linear velocity is distance = velocity x time, and for angular velocity, it is omega = theta / t.

🏃 Linear Velocity Example

Using the example of a runner finishing a 4.2 mile race in 28 minutes and 4 seconds, the average velocity is calculated.

Converting the time to minutes, the average velocity is found to be approximately 1.50 miles per minute or 8.979 miles per hour.

⏱️ Angular Velocity

Angular velocity measures how fast a central angle is changing and is denoted by the lowercase Greek letter omega.

The formula for angular velocity is omega = theta / t, where theta is the central angle in radians and omega is in radians per unit of time.

🔄 Angular Velocity Example

An example of a mechanical arm rotating 1/3 of a rotation in 0.25 seconds is used to calculate angular velocity, which is found to be approximately 8.378 radians per second.

The conversion from degrees to radians is explained and applied in the calculation.

🌀 Linear Velocity around a Circle

The formula for linear velocity around a circle, using arc length, radius, and angular velocity, is discussed.

Different formulas for linear velocity around a circle are presented based on the given information, emphasizing the relationship with angular velocity.

⚙️ Examples

An example involving a tire spinning at 80 revolutions per minute is used to find the angular and linear speed, with detailed unit conversions from inches per minute to miles per hour.

Another example involving individuals on a merry-go-round is used to calculate the angular and linear velocity for different radii, demonstrating the relationship between radius and linear velocity.

🎡 Example

A final example involving individuals on a merry-go-round is used to further illustrate the calculation of angular and linear velocity based on different radii.

The difference in linear velocity for individuals at varying distances from the center is highlighted.