Q.A car takes a turn with a velocity of $50\text{ m s}^{-1}$ on a circular road of radius of curvature $10\text{ m}$. Calculate the centrifugal force experienced by a person of mass $60\text{ kg}$ sitting inside the car.

Pseudo Force – The Trick That Makes Newton's Laws Work Everywhere

Imagine you're sitting in a bus that suddenly lurches forward. What happens? You feel thrown backward against the seat. From the ground outside, a friend sees you stay still while the seat pushes you forward. But inside the bus, it feels like a real force yanked you backward. That feeling is the pseudo force.

The core problem is simple: Newton's laws only work in inertial frames — frames that are either at rest or moving with constant velocity. A bus accelerating forward is a non-inertial frame. Inside it, Newton's first law seems to break: you see an object (your own body) accelerate backward with no visible push. To fix this, we invent a fictitious force — the pseudo force — so that inside the accelerating bus, Newton's laws once again hold.

The Precise Statement

Where:

• $m$ is the mass of the object you're analyzing
• $\vec{a}_{\text{frame}}$ is the acceleration of the non-inertial frame (measured from an inertial frame)
• The minus sign means the pseudo force acts opposite to the frame's acceleration

So if the bus accelerates forward ($\vec{a}_{\text{frame}}$ forward), the pseudo force on every object inside is backward — exactly what you feel.

How to Use It

When solving a problem from inside a non-inertial frame:

1. Identify the acceleration of the frame itself.
2. Add a pseudo force $-m\vec{a}_{\text{frame}}$ on every object you're analyzing.
3. Now treat the frame as if it were inertial — apply Newton's laws normally.

A Concrete Example …