Physics and Mathematics
Centrifugal Force – Definition, Formula and Unit
1. Concept Introduction
When an object moves in a circular path, an observer in the inertial frame (outside the system) perceives an inward centripetal force that keeps the object in circular motion.
However, an observer sitting inside the rotating frame (non-inertial frame) feels as if an outward force is acting on the object — this is called the Centrifugal Force.
It is a pseudo or fictitious force that appears due to the inertia of the body when viewed from a rotating frame.
2. Mathematical Expression
If an object of mass [m] is moving in a circle of radius [r] with angular velocity [\omega],
then the magnitude of the centrifugal force is:
[F_c = m\omega^2r]
Direction: Radially outward from the center of the circular path.
3. Nature of Centrifugal Force
- It is not a real force; it arises only in a rotating (non-inertial) frame.
- It always acts away from the center of rotation.
- It is equal in magnitude and opposite in direction to the centripetal force.
- It helps explain equilibrium in a rotating reference frame.
4. Relation to Centripetal Force
[F_c = -F_{centripetal}]
Hence, in the rotating frame, both forces balance each other.
5. SI Unit and Dimensional Formula
| Quantity | SI Unit | Dimensional Formula |
|---|---|---|
| Centrifugal Force | Newton (N) | [M^1L^1T^{-2}] |
6. Practical Examples
- Drying clothes in a washing machine: Water is thrown outward due to the apparent centrifugal force.
- Passenger moving outward in a turning car: Due to inertia, the body tries to move in a straight line.
- Rotation of a bucket filled with water in a vertical circle: The water stays inside due to apparent outward force balancing gravity at the top.
- Bulging of the Earth at the equator: Centrifugal force due to Earth’s rotation reduces effective gravity.
- Artificial gravity in space stations: Rotation of the station creates a centrifugal effect, simulating gravity.
7. Mathematical Integration
Since [F_c = m\omega^2r] and [v = \omega r],
[F_c = \dfrac{mv^2}{r}]
— exactly equal in magnitude to centripetal force but opposite in direction.
This relation can be derived using the concept of circular motion and vector acceleration.
👉 Refer to topic: Centripetal Force (Physics)
8. Important Formulas to Remember
| Formula | Description |
|---|---|
| [F_c = m\omega^2r] | Magnitude of centrifugal force |
| [F_c = \dfrac{mv^2}{r}] | Expression in terms of linear speed |
| [a_c = \omega^2r] | Centrifugal acceleration |
| [T = \dfrac{2\pi}{\omega}] | Relation between time period and angular velocity |
| [g’ = g – \omega^2r] | Apparent gravity at Earth’s surface (reduced by rotation) |
9. Practice Questions (With Solutions)
Q1. A stone is tied to a string and whirled in a circle of radius [2 m] with angular velocity [5 rad/s]. Find the centrifugal force.
Solution:
[F_c = m\omega^2r = m(5)^2(2) = 50m N]
If [m = 0.5 kg], [F_c = 25 N].
Q2. Find the apparent weight of a person of mass [70 , kg] standing at the equator, given [\omega = 7.27 \times 10^{-5} , rad/s] and [r = 6.37 \times 10^6 , m].
Solution:
[F_c = m\omega^2r] [= 70 (7.27 \times 10^{-5})^2 (6.37 \times 10^6)] [= 2.3 N]
Apparent weight = [mg – F_c = 686.7 – 2.3 = 684.4 N].
Q3. Explain why astronauts in a rotating space station feel weight.
Solution:
The centrifugal force acts outward on their bodies, pressing them against the outer wall — mimicking the sensation of gravity.
10. Conceptual Questions
1. Is centrifugal force a real force?
No, it’s a pseudo force observed only in rotating frames of reference.
2. Why does a person feel pushed outward in a turning car?
Due to inertia, your body tends to continue moving straight while the car turns; in the rotating frame, it feels like an outward force.
3. Can centrifugal force ever act toward the center?
No, by definition it always acts radially outward.
4. Why is centrifugal force important in the design of curved roads?
It helps engineers calculate banking angles and safe speeds to counterbalance apparent outward forces.
5. How does centrifugal force explain the bulging of Earth at the equator?
Due to Earth’s rotation, the outward pseudo force reduces effective gravity at the equator, causing a bulge.
6. What is the relation between centripetal and centrifugal forces?
They are equal in magnitude and opposite in direction — [F_c = -F_{centripetal}].
7. Can centrifugal force balance gravity?
Yes, in rotating systems like space stations, it can simulate artificial gravity.
8. Why is centrifugal force called a pseudo force?
Because it arises only when the observer is in a non-inertial (accelerating or rotating) frame.
9. Does centrifugal force exist in an inertial frame?
No, it appears only in the rotating frame.
10. Why does water remain in a bucket when it’s rotated vertically?
The centrifugal force on water balances or exceeds its weight at the topmost point.
11. FAQs / Common Misconceptions
1. Is centrifugal force opposite to centripetal force?
Yes, but only in the rotating frame. In an inertial frame, there’s only centripetal force.
2. Is centrifugal force a new kind of force?
No, it’s a fictitious effect observed due to inertia in rotating systems.
3. Why does a rotating fan throw off dust particles?
Because the particles lack sufficient centripetal force and move tangentially, appearing to be thrown outward.
4. Does centrifugal force depend on speed?
Yes, it increases with the square of angular speed ([F_c \propto \omega^2]).
5. Why does a passenger feel lighter at the equator?
Because the outward centrifugal force due to Earth’s rotation slightly reduces effective gravity.
6. Can centrifugal force exist without rotation?
No, it exists only in a rotating reference frame.
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