A boy starts from the point a of a rectangle a b c d if he completes one revolution and return to a find the displacement ?
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An object moves from A to D through B and C along a rectangular path as shown in the figure. Find:
(A) the distance covered by the object.
(B) the displacement of the object.
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Solution
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Distance = Length of path travelled
=AB+BC
=15+9
=24km
Displacement = Shortest path from initial to final position
=AC
=
(AB)
2
+(BC)
2
{Pythagoras Theorem}
=
225+81
=17.5km
Explanation:
[tex]Rotation of an Object About a Fixed
Axis
1.1 The Important Stuff
1.1.1 Rigid Bodies; Rotation
So far in our study of physics we have (with few exceptions) dealt with particles, objects
whose spatial dimensions were unimportant for the questions we were asking. We now deal
with the (elementary!) aspects of the motion of extended objects, objects whose dimensions
are important.
The objects that we deal with are those which maintain a rigid shape (the mass points
maintain their relative positions) but which can change their orientation in space. They
can have translational motion, in which their center of mass moves but also rotational
motion, in which we can observe the changes in direction of a set of axes that is “glued to”
the object. Such an object is known as a rigid body. We need only a small set of angles
to describe the rotation of a rigid body. Still, the general motion of such an object can be
quite complicated.
Since this is such a complicated subject, we specialize further to the case where a line
of points of the object is fixed and the object spins about a rotation axis fixed in space.
When this happens, every individual point of the object will have a circular path, although
the radius of that circle will depend on which mass point we are talking about. And the
orientation of the object is completely specified by one variable, an angle θ which we can
take to be the angle between some reference line “painted” on the object and the x axis
(measured counter-clockwise, as usual).
Because of the nice mathematical properties of expressing the measure of an angle in
radians, we will usually express angles in radians all through our study of rotations; on
occasion, though, we may have to convert to or from degrees or revolutions. Revolutions,
degrees and radians are related by:
1 revolution = 360 degrees = 2π radians[/tex]