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Translational Motion
Translational motion is the motion by
which a body shifts from one point in space to another.
One example of translational motion is the
the motion of a bullet
fired from a gun.
An object
has a rectilinear motion when it moves along a straight
line. At any time, t,
the object occupies a position along the line as shown
in the following figure. The distance x, with
appropriate sign, define the position of the object.
When the
position of the object at particular time is known, the
motion of the particle will be known, and
generally is expressed in a form of an equation which
relates distance x, to time t, for example
x = 6t - 4, or a graph.
Motion in two or three dimensions is more
complicated. In two dimensions, we need to specify two
coordinates in order to fix the position of any object.
The following figure shows a simple example of
projectile motion: a ball rolling off a table. Let us
define the horizontal direction as the x-axis and
the vertical direction as the y-axis.
Consider a ball initially rolling on off a flat table
with an initial velocity of 10 m/s.
While the ball is on the table we observe
that the initial x-component of velocity (v0x)
is 10 m/s (constant), the initial y-component of
velocity is 0 m/s, the x-component of
acceleration is 0 m/s2 and the y-component
of acceleration is 0 m/s2. The components of
acceleration and velocity are those parts of the
velocity or acceleration that points in the x or
y direction.Let us
observe what happens the instant the ball leaves the
table.
The initial velocity in the y-direction is
still zero and the initial velocity in the x-direction
remains 10 m/s. However, the ball is no longer in
contact with the table and it falls freely. The
gravitational acceleration of the ball is down. In this
case, the motions in the horizontal and vertical
directions should be analyzed independently.
Horizontally, there is no acceleration in the horizontal
direction, therefore, the x-component of velocity
is constant
In
the vertical direction there is an acceleration equal to
the acceleration of gravity. Therefore, the velocity in
the vertical direction changes as below
Rotational Motion
Rotational motion deals only with
rigid bodies. A rigid body is an object that retains
its overall shape, meaning that the particles that make
up the rigid body remain in the same position relative
to one another. A wheel and rotor of a motor are common
examples of rigid bodies that commonly appear in
questions involving rotational motion.
Circular Motion
Circular
motion is a common type of rotational motion. Like
projectile motion we can analyze the kinematics and
learn something about the relationships between
position, velocity and acceleration. Newton’s first law
states that an object in motion remains in motion at
constant velocity unless acted upon by an outside force.
If the force is applied perpendicular to the direction
of motion, only the direction of velocity will change.
If a force constantly acts perpendicular to a moving
object, the object will move in a circular path at
constant speed. This is called uniform circular motion.
The circular motion of a rigid body
occurs when every point in the body moves in a circular
path around a line called the axis of rotation,
which cuts through the center of mass as shown in the
following figure.
Uniform Circular Motion
An online simulation to measure the
position, velocity, and acceleration (both
components and magnitude) of an object undergoing
circular motion.
Translational
Motion Versus Rotational Motion
There is a strong analogy
between rotational motion and standard translational
motion. Indeed, each physical concept used to analyze
rotational motion has its translational concomitant.
Moment of Inertia
Discover the relationships between
angular velocity, mass, radius and moment of inertia for
collections of point-masses, rings, disks, and more
complex shapes.
Torque and Moment of Inertia
Calculate net torque and moment of
inertia based on the positions of the objects and the
mass of a bar.
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