Winsome Publication: Engineering Physics I

Q.1 What do you understand by a frame of reference? Is earth an inertial frame of reference? If not, why? (AKTU. 2007-08)

Ans. Frame of Reference: -

In order to specify the location of a point object or an event in space, we require a coordinate system. We choose a point of origin and directions for three axes. Therefore, the location of a point object or an event is expressed in terms of three real numbers, called coordinates of that point object with respect to the origin. For complete information about an event, we must not only know about its true location or position, but also its correct time of occurrence. Thus, we need another coordinate axis that of time. Such a coordinate system with respect to which we measure the position of a point object or an event is called a frame of reference. The motion of a point is completely described if we express the three point coordinates as function of time. A point is at rest relatively to our frame of reference if these three functions are constant. The frames of reference are of two types:

(1) Inertial or unaccelerated frames of reference.

(2) Non-inertial or accelerated frames of reference.

Earth as a Inertial Frame of Reference: -

The frames of reference which Newton’s law of inertia and other laws of Newtonian mechanics hold good are called inertial frames of reference or simply inertial frames. Unaccelerated frames are inertial frames. Inertial frame is also defined as the frame in which a body at rest or moving with uniform velocity and not under the influence of any force, remain at rest or moving with the same uniform velocity.

For our ordinary purpose, the earth serves well enough as an inertial frame of reference and hence, also the interior of a vehicle, such as train, car etc. moving smoothly and with a constant velocity on its surface.

Q.2 Differentiate inertial and noninertial frames of reference and show that inertial frames move with constant velocity relative to each other. (AKTU. - 2005-06)

Ans: Inertial frames: -

In this frame, bodies obey Newton’s law of inertia and other laws of Newtonian mechanics. In inertial frame, a body not acted upon by external force, is at rest or moves with a constant velocity. The laws of physics will be same for all observers in this frame of reference.

Non-inertial frames: -

In this frame, the Newton’s laws are not valid and a body, not acted upon by an external force is accelerated.

Let us consider two inertial systems S and S`. The system S` moves with a velocity v along positive direction of X-axis. From figure we have x` = x –vt, y` =y, z` = z and t` = t. let u`x, u`y, u`z represents component of velocity in S‘ system. Then

(where ux =dx/dt)

..........(1)

Similarly

..........(2)

And

..........(3)

from eq.(1), (2) and (3) we get acceleration of a particle in system S is same as in S`, so, we conclude that inertial frames move with constant velocity relative to each other.

Q.3. What do you understand by variant and invariant under the Galilean Transformations? (AKTU. - 2011 - 12)

Ans. When the variation measured by the observers in time frames are the same then it is called invarient otherwise varient under Galilean transformations.

Q.4 Show that the distance between any two points in two inertial frames is invarient under Galilean transformation. (AKTU. - 2007-08)

Ans. Suppose a frame of reference S¢ is moving with velocity v relative to a frame S at rest. Let the coordinates of two points in frame S be (x1, y1, z1) and (x2, y2, z2), while those in frame S¢ be (x1¢, y1¢, z1¢) and (x2¢, y2¢, z2¢).

From Galilean transformation, we have