System of Particles and Rotational Motion 1

Question 1

what is a rigid body

Answer 1

Ideally a
rigid body is a body with a perfectly definite and
unchanging shape. The distances between all pairs of
particles of such a body do not change.

Question 2

what is translational motion

Answer 2

In pure translational motion at any
instant of time all particles of the body have
the same velocity.

Question 3

what is rotationa motion

Answer 3

motion of a body is said to be rotational motion if the body rotates about a fixed axis such that each particle of the body is performing circular motion iwth its centre in the axis of rotation

The axis about which body rotates is axis of rotation.

The
motion of a rigid body which is pivoted or
fixed in some way is rotation.

Question 4

what is precession

Answer 4

change in the axis of rotation of body such that the axis of rotation prescribes a cone with the vertex (whr it touches the ground)

Question 5

centre of mass

Answer 5

centre of mass of a system of particle is the point where the entire mass of the system is considered to be concentrated and at which all external forces are considered to be acting on.

• it depends on mmass distrubution within the body

-it may be present outside the body: ex: ring, horshoe

Question 6

motion of centre of mass is independent of internal force

Answer 6

A projectile, following the usual parabolic
trajectory, explodes into fragments midway in
air. The forces leading to the explosion are
internal forces. They contribute nothing to the
motion of the centre of mass. The total external
force, namely, the force of gravity acting on the
body, is the same before and after the explosion.
The centre of mass under the influence of the
external force continues, therefore, along the
same parabolic trajectory as it would have
followed if there were no explosion.

Question 7

explain the law with example” if fext=0, then change in momentum=0, for radium nucleus

Answer 7

let us consider the
radioactive decay of a moving unstable particle,
like the nucleus of radium. A radium nucleus
disintegrates into a nucleus of radon and an
alpha particle. The forces leading to the decay
are internal to the system and the external
forces on the system are negligible. So the total
linear momentum of the system is the same
before and after decay. The two particles
produced in the decay, the radon nucleus and
the alpha particle, move in different directions
in such a way that their centre of mass moves
along the same path along which the original
decaying radium nucleus was moving

Question 8

explain the law with example” if fext=0, then change in momentum=0, for binary stars

Answer 8

In astronomy, binary (double) stars is a
common occurrence. If there are no external
forces, the centre of mass of a double star
moves like a free particle, as shown in Fig.7.14
(a). The trajectories of the two stars of equal
mass are also shown in the figure; they look
complicated. If we go to the centre of mass
frame, then we find that there the two stars
are moving in a circle, about the centre of
mass, which is at rest. Note that the position
of the stars have to be diametrically opposite
to each other [Fig. 7.14(b)]. Thus in our frame
of reference, the trajectories of the stars are a
combination of (i) uniform motion in a straight
line of the centre of mass and (ii) circular
orbits of the stars about the centre of mass.