Circular Motion Equations Calculator

What is Circular Motion?

Circular motion is a type of motion in which an object moves in a circular path or orbit. It is characterized by a constant speed but continuously changing velocity due to the constant change in direction. This type of motion is fundamental in many natural phenomena and technological applications, from planetary orbits to the operation of centrifuges.

Formulas

The key equations describing circular motion are:

1. \[ v = \frac{2\pi r}{T} = 2\pi rf \]
2. \[ a_c = \frac{v^2}{r} = \omega^2 r \]
3. \[ T = \frac{2\pi r}{v} = \frac{1}{f} \]

Where:

• \(v\) is the tangential velocity (m/s)
• \(r\) is the radius of the circular path (m)
• \(T\) is the period of rotation (s)
• \(f\) is the frequency of rotation (Hz)
• \(a_c\) is the centripetal acceleration (m/s²)
• \(\omega\) is the angular velocity (rad/s)

Calculation Steps

Let's calculate the velocity of an object in circular motion with a radius of 5 m and a period of 2 s:

1. Identify the known values:
   • Radius (r) = 5 m
   • Period (T) = 2 s
2. Apply the velocity formula: \[ v = \frac{2\pi r}{T} \]
3. Substitute the known values: \[ v = \frac{2\pi \cdot 5 \text{ m}}{2 \text{ s}} \]
4. Perform the calculation: \[ v = 5\pi \approx 15.71 \text{ m/s} \]

Example and Visual Representation

Let's visualize the circular motion with our calculated example:

This visual representation shows:

• The circular path of the object
• The radius of 5 meters
• The tangential velocity of approximately 15.71 m/s
• The period of 2 seconds for one complete revolution