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System of Particles and Rotational Motion

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Physics Part I

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Class 10 Class 12
A car weighs 1800 kg. The distance between its front and back axles is 1.8 m. Its centre of gravity is 1.05 m behind the front axle. Determine the force exerted by the level ground on each front wheel and each back wheel.

Mass of the car, m = 1800 kg 

Distance between the front and back axles, d = 1.8 m

Distance between the centre of gravity and the back axle = 1.05 m 

The various forces acting on the car are shown in the following figure.


Rf and Rare the forces exerted by the level ground on the front and back wheels respectively. 

At translational equilibrium, 

Rf + Rb = mg 

            = 1800 × 9.8

            = 17640 N                               ... (i)

For rotational equilibrium, on taking the torque about the C.G., we have

R(1.05) = R(1.8 - 1.05)

        straight R subscript straight b over straight R subscript straight f space equals space 7 over 5

          Rb = 1.4 Rf                                 ...(ii) 

Solving equations (i) and (ii), we get

1.4Rf + Rf = 17640 

            Rf = 7350 N 

∴          Rb = 17640 – 7350

                = 10290 N 

Therefore, the force exerted on each front wheel = 7350 over 2  =  3675 N.
The force exerted on each back wheel = 10290 over 2 =  5145 N 

Is it necessary that there should be matter at the centre of mass of system?

No, it is not necessary that there be matter at the centre of mass of the system.

For e.g., if two equal point masses are separated by certain distance, the centre of mass lies at the mid point of two point masses and there is no mass at that point.

Is it necessary for centre of mass to lie within the body?

No, centre of mass needs not to lie within the body. It is not necessary that the total mass of the system be actually present at the centre.

The position of the centre of mass is calculated using the usual Newtonian type of equations of motion. 

What is the need of centre of mass?

Newton’s second law of motion is strictly applicable to point masses only. To apply the Newton's law of motion to rigid bodies, the concept of centre of mass is introduced.

The concept of centre of mass of a system enables us to discuss overall motion of the system by replacing the system by an equivalent single point object. 

What is the significance of defining the center of mass of a system?

The motion of n particle system can be reduced to one particle motion.

An equivalent single point object would enable us to discuss the overall motion of the system. 

Define centre of mass.

Centre of mass of a body or a system of bodies is a point at which the entire mass of the body or system is supposed to be concentrated.