Explanation
Velocity of centre of mass of a body is constant when no external force acts on the body. If there is no external torque, it does not mean that no external force acts on it.
As the concept of centre of mass is only theoretical, therefore in practice no mass may lie at the centre of mass. For example, centre of mass of a uniform circular ring is at the centre of the ring where there is no mass.
Initially the electron and proton were at rest so their centre of mass will be at rest. When they move towards each other under mutual attraction then velocity of centre of mass remains unaffected because external force on the system is zero.
The position of centre of mass of a body depends on shape, size and distribution of mass of the body. The centre of mass does not lie necessarily at the centre of the body.
Through bending weight of opponent is made to pass through the hip of judo fighter to make its torque zero.
The position of centre of mass of electron and proton remains at rest. As their motion is due to internal force of electrostatic attraction, which is conservative force. No external force is acting on the two particles, therefore centre of mass remain at rest.
At the centre of earth, g = 0. Therefore a body has no weight at the centre of earth and have no centre of gravity (centre of gravity of a body is the point where the resultant force of attraction or the weight of the body acts), Hut centre of mass of a body depends on mass and position of particles and is independent of weight.
Explosion is due to internal forces. As no external force is involved, the vertical downward motion of centre of mass is not affected.
The moment of inertia of a particle about an axis of rotation is given by the product of the mass of the particle and the square of the perpendicular distance of the particle from the axis of rotation. For different axis, distance would be different, therefore moment of inertia of a particle changes with the change in axis of rotation.
There is a differences between inertia and moment of inertia of a body. The inertia of a body depends only upon the mass of the body but the moment of inertia of a body about an axis not only depends upon the mass of the body but also upon the distribution of mass about the axis of rotation.
When a person is high up on the ladder, than a large torque is produced due to his weight about the point of contact between the ladder and the floor. Whereas when he starts climbing up. The torque is small. Due to this reason, the ladder is more apt to slip, when one is high up on it.
In sliding down, the entire potential energy is converted into kinetic energy. While in rolling down some part of potential energy is converted into K.E. of rotation. Therefore linear velocity acquired is less.
In rolling all points of rigid body have the same angular speed but different linear speed.
Rolling occurs only on account of friction which is a tangential force capable of providing torque. When the inclined plane if perfectly smooth, body will simply slip under the effect of its own weight
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