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COMPARING
TRANSLATIONAL
AND ROTATIONAL
MOTION
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OBJECTIVES:
By the end of the discussion,
learners are expected to:
1. Compare and contrast
translational and rotational
motion in terms of linear and
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WHAT IS
TRANSLATIONAL
MOTION?
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TRANSLATIONAL MOTION
 Translational motion occurs when an object
moves from one location to another along a
straight path.
 Occurs when an object moves from one
point to another—either in a straight line
(rectilinear motion) or along a curved path
(curvilinear motion).

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Described using linear quantities:
 Linear Displacement – Change in
position measured in meters (m)
 Linear Velocity – Rate of change
in position (m/s)
 Linear Acceleration – Rate of
change in velocity (m/s²)
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WHAT IS ROTATIONAL
MOTION?
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ROTATIONAL MOTION
Rotational motion describes
movement around a fixed axis.
Objects follow a circular path rather
than a straight line.
Rotational motion occurs when an
object spins around an axis. This axis
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Described using angular quantities:
 Angular Displacement – Change
in angle measured in radians (rad)
 Angular Velocity – Rate of change
in angle (rad/s)
 Angular Acceleration – Rate of
change in angular velocity (rad/s²)
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UNITS AND MEASUREMENTS
Different units reflect the fundamental
differences between linear and angular
measurements.
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DISPLACEMENT:
LINEAR VS. ANGULAR
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Linear Displacement (x)
 Definition: The change in position
of an object measured along a
straight line.
 Unit of Measurement: Meters
 Formula
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SAMPLE PROBLEMS:
1. A toy car starts at a position of 3m on a
one-dimensional track. It moves to the
right and stops at a position of 12m.
What is the linear displacement of the
car?
2. A runner starts at a landmark, sprints
150m due East, and then turns around to
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SAMPLE PROBLEMS:
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Angular Displacement ()
 Definition: The angle through
which an object rotates around an
axis.
 Unit of Measurement: Radians
(rad)
 Formula:
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SAMPLE PROBLEM:
1. A robotic arm is tracking coordinates on
a circular welding line. It starts at an
initial angular position of rad and
rotates counterclockwise to a final
position of rad. What is the arm's
angular displacement?
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SAMPLE PROBLEMS:
1. A boy runs about 400 meters around a
circular track. 35 meters is the radius of
the track. What will be the angular
displacement?
2. A cyclist rides around a circular track that
has a radius of 50m. If the cyclist travels
a linear distance (arc length, 150m along
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ACCELERATION:
LINEAR VS. ANGULAR
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Linear Acceleration ()
 Definition: The rate at which an
object's velocity changes with respect
to time as it moves along a straight-
line path
 Unit of Measurement: m/s²
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SAMPLE PROBLEMS:
1. A train starts from rest and accelerates
uniformly along a straight track to a
velocity of 24 m/s. What is its linear
acceleration?
2. A car traveling at a high speed of 35 m/s
slams on the brakes and comes to a
complete, uniform stop 5 seconds . What
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SAMPLE PROBLEMS:
1. A delivery truck speeds up uniformly from
54 km/h to 90 km/h over a duration 4
seconds. Find its linear acceleration in
m/s².
2. An experimental maglev capsule's linear
velocity along a test track changes over
time according to the function v(t) = 3t² + 2t
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Angular Acceleration ()
 Definition: Angular acceleration is the rate
at which an object's angular velocity
changes over time. It measures how
quickly a spinning object speeds up, slows
down, or changes its axis of rotation
 Unit of Measurement: rad/s²
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SAMPLE PROBLEMS:
1. An exercise wheel starts from rest and is
spun up uniformly to an angular velocity
of 36 rad/s over a time span of 12
seconds. What is its angular
acceleration?
2. A blender blade spinning at an angular
velocity of 80 rad/s is switched off. It
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SAMPLE PROBLEMS:
1. A specialized laboratory
centrifuge spins up such that its
angular position is given by the
function (t) = t³ - 2t² + 4t (where is
in radians and t is in seconds).
Determine its angular
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ANY
QUESTION?