Pseudo force (Class 11): see it in a train, a lift and a turntable
A pseudo force is the force you have to add so that Newton's second law works in an accelerating frame. It does not come from any object pushing, yet you feel it when a bus brakes. These labs let you stand on the ground and inside the vehicle and compare what each observer measures.
NCERT Class 11 Physics, Chapter 4 (Laws of Motion), non-inertial frames in the exercises. Every lab below runs in 3D in your browser or on a phone, in English and Hindi.
Try the labs
Pseudo force in an accelerating train: hanging bob, sliding block and balloon · free · Chapter 4
To see why an observer inside an accelerating train feels a backward "pseudo force", and to use it to find the angle of a hanging bob, the slipping of a block and the lean of a balloon.
Coin on a rotating turntable: friction, centrifugal pseudo force and slipping · plan · Chapter 4
To see what keeps a coin moving in a circle on a turntable, when it slips, and how the same situation is described by an observer on the ground and by an observer on the rotating turntable.
Apparent weight in an accelerating lift · plan · Chapter 4
To understand apparent weight in a non-inertial frame (accelerating lift).
Atwood machine and pulley systems · plan · Chapter 4
To apply Newton's second law to connected bodies over a pulley and find acceleration and string tension.
Banked road: maximum safe speed · plan · Chapter 4
To understand why roads are banked and find the speed limits for a car turning on a banked curve with friction.
Block on a movable wedge · plan · Chapter 4
To analyse a block sliding down a smooth wedge which is itself free to slide on a smooth horizontal floor.
Conical pendulum · plan · Chapter 4
To analyse the conical pendulum: relation between speed, cone angle, tension and period.
Block on an inclined plane: static and kinetic friction · plan · Chapter 4
To find the coefficient of static friction from the angle of repose and to study motion of a block down a rough incline.
Recoil of a gun: conservation of momentum · plan · Chapter 4
To verify conservation of linear momentum using the recoil of a gun.
Movable pulley and string constraints · plan · Chapter 4
To solve a pulley system with a movable pulley using the string-length constraint and Newton second law.
Two blocks with friction: when does the top block slip? · plan · Chapter 4
To study static and kinetic friction between two stacked blocks and find the maximum force before the top block slips.
What is a pseudo force?
Newton's laws hold only in an inertial frame, one that is not accelerating. If you sit in a frame that accelerates with a₀, a body at rest on the ground appears to accelerate with −a₀ and no real force explains it. To keep F = ma usable you add an imaginary force of −m a₀. That is the pseudo (fictitious) force.
It has no reaction partner, it exists only for the accelerating observer, and it always points opposite to the acceleration of the frame. An observer on the ground never needs it.
F_pseudo = −m a₀effective gravity g_eff = √(g² + a₀²)
Pendulum and balloon in an accelerating train
A bob hanging from the roof of a train that accelerates forward with a swings backwards and settles at an angle where tan θ = a / g. From the ground the tension has a horizontal part m a (it accelerates the bob) and a vertical part m g. Inside the train the bob is at rest because tension, weight and the pseudo force −ma balance.
A helium balloon does the opposite: it moves forward, because the air in the cabin is pushed back and the lighter balloon is pushed the other way. The cart lab shows both, with a frame toggle for the two observers.
tan θ = a / gT = m √(g² + a²)
Will the block slip?
A block on the floor of the accelerating cart feels a pseudo force m a backwards. Friction can supply at most μ m g. The block stays at rest relative to the cart while a ≤ μ g and slides backwards once a > μ g.
a_max = μ g
Centrifugal force on a turntable
The rotating frame is accelerating too, towards the axis. A coin on a turntable moves in a circle because friction supplies the centripetal force m ω² r. For an observer rotating with the turntable the coin is at rest, so a centrifugal pseudo force m ω² r acts outwards and friction balances it.
The coin slips when ω² r exceeds μ g, so ω_max = √(μ g / r). It then leaves along the tangent, not radially, which is what the lab shows from the ground frame.
F_centrifugal = m ω² rω_max = √(μ g / r)v_max = √(μ r g)
Frequently asked questions
Is pseudo force a real force?
No. It is not caused by any object and has no reaction. It is added by an observer in an accelerating frame so that Newton's second law can still be used there. An observer in an inertial frame never needs it.
Why does the pendulum in an accelerating train tilt backwards?
Seen from the ground the bob must accelerate forward with the train, so the string tilts until the horizontal part of the tension equals m a. Seen from the train the pseudo force −ma pushes the bob backwards. Both give tan θ = a / g.
What is the difference between centripetal and centrifugal force?
Centripetal force is a real net force towards the centre (friction, tension or gravity) seen from an inertial frame. Centrifugal force is the outward pseudo force seen only by an observer rotating with the body.
At what speed does a coin fly off a rotating turntable?
When m ω² r becomes larger than the maximum friction μ m g, that is when ω = √(μ g / r). The coin then moves in a straight line along the tangent.
Does the pseudo force depend on the mass?
Yes, it is m times the acceleration of the frame, just like gravity, so the acceleration it produces is the same for every body.