How To Find Tangential Force: Several Approaches And Problem Examples


Tangential force is the force acting on a body in a circular motion in the tangential direction of a curved path.

Let’s answer, How to find tangential force A tangential force is the follow up of a tangential acceleration which is always at right angle to the radius which originate from the axis of rotation. In pursuance for there to be a tangential force, it is necessary that the tangential velocity changes.

Where tangential acceleration is:-

Suppose a particle performing a circular motion is not uniform. And it is variable. Then in such conditions, the particle in a circular motion will have tangential acceleration along with the centripetal acceleration or radial acceleration. If the particle in a small interval of time, and the change in the tangential velocity of the particle will be, then the tangential acceleration of the particle will be given as:-

A particle in tangential acceleration

Now, for the given time interval, If it is infinitesimally small, than the tangential acceleration at that point will be:-

aT=dv/dt

And, the radial acceleration of the particle will be:-

aR=v2/r

Here the tangential acceleration and the radial acceleration are at right angle to each other. Hence the magnitude of the resultant acceleration of the p[article in motion is given as:-

In the variable circular motion of the particle, the tangential acceleration and radial acceleration both are variable. Hence, we can say that the resultant acceleration of particle a is also variable, and it is not directed towards the center of the circle.

How do you find tangential force in a circular motion

How to find tangential force:- To find the tangential force of a particle in a circular motion. Lets get down to a particle P whose orientation with respect to the origin O is r. Now a force of 90 N (tangential force) acts on the particle, then the moment of the force or torque is acting on the particle with respect to the origin O. Now the relation between and r and F is given as:-

how to find tangential force
A particle in circular motion with origin as O

The magnitude is given as:-

 Where is the angle between vector r and F.

From here, we can find tangential force as:-

What is the tangential component of a force

The force acting on an object which is in contact with a surface of another body can be resolved into two components, respectively. There is One component which is perpendicular to the surface at a given occasion this is the normal force, and another component, is parallel to the surface this the tangential force. Specifically, the mass of the body having weight w = mg is on inclined plane adjusted at an angle to the horizontal. It  will have normal and tangential forces of:

Fn=mgcosθ

Ft=mgsinθ

Here Ft is the tangential force that acts at right angles to the tangent. Tangential force can alternate the direction of the motion of body without alternating its velocity.

Problem Examples Based On Tangential Force

Q. Explain the reason in the given condition which is the cause of centripetal force in them? (i) In rotating a car, (ii) while moving a ball which is tied to strings in a circular motion, (iii) in earth’s revolution around the sun, (iv) in the revolution of an electron around the nucleus.

Ans. (i) From friction between tires and road, om tension in the string, (iii) from the (ii) gravitational force exerted by sun on earth, (iv) in the revolution of an electron around the nucleus there is electrostatic force of attraction, between nucleus and electron.

Q. In the rain, generally, the scooter slips at the turning of a road; why?

Ans. In the rain, generally, the scooter slips at the turning of a road because the necessary centripetal force is not provided. As On the wet road, the friction between tire and road is lessen.

Q. A small smooth ball is placed on a smooth circular disc. Explain why, when the disc is turn round, the ball falls down?

Ans. Due to the absence of friction between the ball and the disc, the centripetal force is not provided to the ball.

Q. A child riding on a merry go round  bear down side of his seat, which result in radially outward motion. Explain why?

Ans. As the child presses the side of his seat radially outwards, the side of the seat presses the child radially inwards (Newton’s third law), thus providing him the required centripetal force for his circular motion.

Q. Do the clockwise rotation or anticlockwise rotation in a uniform circular motion defines the direction of the centripetal force?

Ans. No, the direction of the acceleration vector, or force, is radially inwards for either case.

Q. Consider a particle which is moving uniformly on a circle path. The particle on circular path experiences two sort of forces. One is the centripetal force, this force is directed towards the center. The other force is centrifugal force, this force is equal to centripetal and directed in opposite direction from the center. Comment, whether the two forces keep the the particle in equilibrium position or not.

Ans. This statement is entirely wrong.

A particle. In uniform circular motion is not in equilibrium. It has a radial acceleration (v²/r), or a centripetal force (mv²/r), acting radially inwards towards the center. Where the resultant force on the particle is not zero. Hence, there is no question of any radially outward force balancing the radially inward force.

However, when an observer is rotating with the particle (non-inertial frame), for him, the particle appears at rest. This observer, therefore, invokes in his frame a ‘centrifugal force’ which balances the inward force. Thus, centrifugal force is not a real force but arises from the non-inertial nature of the observer himself.

Q. If we consider a thin wheel in motion, then it can be in upright position on its rim for a appreciable period of time when turn over and over with an appreciable velocity. Whereas it will fall from its upright position if there is any slightest of disturbance when it is stationary position. Explain.

Ans. When the wheel rolls, its angular momentum is conserved.

In practice, there is a loss in angular velocity and hence in angular momentum due to friction. But the wheel does not fall so long there is angular momentum in it. The stationary upright wheel is in ‘unstable’ equilibrium, hence falls by a slight disturbance.

Q. Why are there two propellers in a helicopter?

Ans. There are two propellers in a helicopter because if a helicopter would have only one propeller:-

Then the angular momentum would be conserved for it, then due to this conservation, the helicopter themselves would have rotated in the opposite direction.

Riya Pandey

I am Riya Pandey. I have completed Post Graduation in physics in 2021. Currently I am working as a Subject Matter Expert in Physics for Lambdageeks. I try to explain Physics subject easily understandable in simple way.

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