Calculating Angular and Linear Velocity for Spinning Particles

TLDR; Example demonstrates how to calculate angular and linear velocity for particles spinning on a disc with varying distances from the center.

⚙️ Particles' Positions

Two particles are spinning on a disc, with one 12 centimeters away from the center and the other 15 centimeters away.

These particles can be visualized on concentric circles, each representing their distance from the center of the disc.

🔄 Angular Velocity Calculation

The angular velocity (omega) is calculated using the formula omega = theta / t, where theta represents the angle of rotation and t is the time taken.

It's noteworthy that this formula does not involve the radius, making the angular velocity the same for both particles.

With a rotation time of 6 seconds, the angular velocity is found to be pi/3 radians per second.

📏 Linear Velocity Calculation

The linear velocity is determined by using the formula v = r x omega, where r is the radius and omega is the angular velocity.

As the particles have different radii, their linear velocities differ. For the particle 12 centimeters away, the linear velocity is calculated to be 4/pi centimeters per second, and for the particle 15 centimeters away, it's 5/pi centimeters per second.

🔄 Alternative Formula for Linear Velocity

An alternative formula for linear velocity, v = r x omega, is mentioned which would have made the calculation a little less work, as omega (angular velocity) was already found in the earlier step.