6.1 – Circular Motion

Hey there, physics enthusiasts! Today, we're diving into the fascinating world of circular motion. This topic is a real game-changer in physics, as it helps us understand everything from the spin of a merry-go-round to the orbit of planets. Let's break it down and make it as clear as a perfect circle!

Period and Frequency

First up, let's talk about period and frequency. These two concepts are like two sides of the same coin in circular motion.

Period (T)

The period is the time it takes for an object to complete one full revolution. Think of it as "How long does it take to go around once?"

Frequency (f)

Frequency, on the other hand, is the number of revolutions completed in one second. It's like asking, "How many times does it go around in a second?"

Angular Displacement and Angular Velocity

Now, let's move on to some angular measurements. These are crucial for describing circular motion accurately.

Angular Displacement (θ)

Angular displacement is the angle through which an object rotates. It's measured in radians (rad) and gives us an idea of how far around the circle an object has moved.

Angular Velocity (ω)

Angular velocity tells us how fast the angular position is changing. It's the rate of change of angular displacement with respect to time.

$$ \omega = \frac{\Delta \theta}{\Delta t} $$

Centripetal Force and Acceleration

Here's where things get really interesting! Centripetal force and acceleration are what keep objects moving in a circular path.

Centripetal Force

Centripetal force is the force that makes a body follow a curved path. It's always directed toward the center of the circle.

The magnitude of centripetal force is given by:

$$ F_c = \frac{mv^2}{r} = mr\omega^2 $$

Where:

• m is the mass of the object
• v is the linear velocity
• r is the radius of the circular path
• ω is the angular velocity