Calculating Centrifugal Force
Force is required to make an object move, and force acts differently on objects depending on the type of motion it exhibits. In the case of curvilinear motion, a special force comes into the picture, i.e., centripetal force – literally meaning “centre seeking.” Centripetal force is the force acting towards the centre of the circular path.
Centrifugal force definition
Centrifugal force is the inertia force that arises in each rotating object. It is only required in a rotating reference frame - or, in other words, when we look at the system from the point of view of the object in motion.
According to Newton's first law, if no force acts on an object, it moves in a straight line. For rotation to occur, a centrifugal force - acting outwards from the center of rotation - must be applied.
For example, you can imagine a rock whirled round on a string. The centrifugal force is the force that prevents it from moving towards the center of rotation (that is, towards your hand).
Centrifugal force equation
If you know the velocity of the object, simply use the following formula:
F = mv²/r
where:
- F is the force expressed in newtons;
- m is the mass of the object;
- v is the velocity; and
- r is the radius.
If you know only the angular velocity ω, you can recalculate it to normal velocity by simply multiplying it by the circumference of the circular path. Use the following equation:
v = ω2πr
in case your ω is in Hz (1/s).
Or the formula:
v = ωr
for ω in rad/s.
Or simply type the values of ω and r into our calculator.
Example
Centrifugal Force Calculation
Centrifugal force is the apparent force that acts outward on a body moving around a center, arising from the body's inertia. It is a fictitious force that we feel when we are in a rotating reference frame, pushing us away from the axis of rotation.
The general approach to calculating centrifugal force includes:
- Identifying the mass of the object.
- Knowing the velocity of the object moving in a circle.
- Determining the radius of the circular path.
- Applying the formula for centrifugal force to calculate the result.
Centrifugal Force Formula
The general formula for centrifugal force is:
\[ F_c = \frac{{m \cdot v^2}}{{r}} \]Where:
- m is the mass of the object (in kilograms, kg).
- v is the velocity of the object (in meters per second, m/s).
- r is the radius of the circular path (in meters, m).
Example:
If an object of mass 2 kg is moving at a velocity of 10 m/s in a circle with a radius of 5 m, the centrifugal force is:
- Step 1: Square the velocity: \( v^2 = 10^2 = 100 \, \text{m}^2/\text{s}^2 \).
- Step 2: Multiply by the mass: \( m \cdot v^2 = 2 \cdot 100 = 200 \, \text{kg} \cdot \text{m}^2/\text{s}^2 \).
- Step 3: Divide by the radius: \( F_c = \frac{{200}}{{5}} = 40 \, \text{N} \).
Centrifugal Force with Changing Radius
If the radius of the circular path changes, the centrifugal force also changes. The relationship between centrifugal force and radius is inversely proportional. As the radius increases, the centrifugal force decreases, and vice versa.
Example:
If the mass of the object remains the same but the radius is doubled, the centrifugal force will be halved. For example, with a mass of 2 kg, velocity of 10 m/s, and a radius of 10 m, the centrifugal force is:
- Step 1: \( v^2 = 10^2 = 100 \, \text{m}^2/\text{s}^2 \).
- Step 2: \( m \cdot v^2 = 2 \cdot 100 = 200 \, \text{kg} \cdot \text{m}^2/\text{s}^2 \).
- Step 3: \( F_c = \frac{{200}}{{10}} = 20 \, \text{N} \).
Real-life Applications of Centrifugal Force
Calculating centrifugal force is important in various practical applications, such as:
- In centrifuges, where the centrifugal force helps separate substances of different densities.
- In vehicle turns, where centrifugal force is felt by passengers as they are pushed outward from the curve.
- In roller coasters and amusement park rides, where centrifugal force gives the feeling of being thrown outward during high-speed turns.
Common Units of Centrifugal Force
SI Unit: The standard unit of centrifugal force is the newton (N).
Centrifugal force can also be expressed in other units, such as pounds-force (lbf), but the SI unit (newtons) is commonly used in most calculations.
Common Operations with Centrifugal Force
Uniform Circular Motion: When an object moves with constant velocity in a circle, the centrifugal force remains constant.
Variable Velocity: If the velocity of the object changes, the centrifugal force will also change accordingly.
Effect of Radius: If the radius of the circular path increases, the centrifugal force decreases, and vice versa, keeping the velocity constant.
| Problem Type | Description | Steps to Solve | Example |
|---|---|---|---|
| Calculating Centrifugal Force from Mass and Velocity | Finding the centrifugal force when given the mass of the object, velocity, and radius. |
|
For an object of mass \( 2 \, \text{kg} \) moving at \( 10 \, \text{m/s} \) in a circle of radius \( 5 \, \text{m} \), the centrifugal force is \( F_c = \frac{{2 \cdot 10^2}}{{5}} = 40 \, \text{N} \). |
| Calculating Centrifugal Force with Changing Radius | Finding the centrifugal force when the radius changes but the velocity stays constant. |
|
If an object of mass \( 3 \, \text{kg} \) moves at \( 15 \, \text{m/s} \) in a circle with radius \( 10 \, \text{m} \), the centrifugal force is \( F_c = \frac{{3 \cdot 15^2}}{{10}} = 67.5 \, \text{N} \). |
| Calculating Centrifugal Force with Constant Speed and Mass | Finding the centrifugal force when the mass and velocity remain constant but the radius varies. |
|
If a mass of \( 5 \, \text{kg} \) moves at \( 8 \, \text{m/s} \) in a circle with a radius of \( 4 \, \text{m} \), the centrifugal force is \( F_c = \frac{{5 \cdot 8^2}}{{4}} = 80 \, \text{N} \). |
| Real-life Applications | Applying centrifugal force to solve practical problems in motion, such as vehicle turns or rotating systems. |
|
If a car of mass \( 1000 \, \text{kg} \) moves at \( 20 \, \text{m/s} \) around a circular track with a radius of \( 50 \, \text{m} \), the centrifugal force is \( F_c = \frac{{1000 \cdot 20^2}}{{50}} = 8000 \, \text{N} \). |
