Translational and Rotational Motion PDF.

Translational and Rotational Motion PDF.

• 1.
  TRANSLATIONAL & ROTATIONAL MOTION Lesson2
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  Motion is theobservable change in position of a body with respect to a reference point.
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  TYPES OF MOTION Motionwhere an object moves from one place to another. TRANSLATIONAL Motion where an object spins or rotates around an axis. ROTATIONAL
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  TRANSLATIONAL • Translational motionhappens when an object moves from one place to another. • All parts of the object move in the same direction. EXAMPLES: • Walking • Running • Moving train • Sliding cabinet Linear Quantities • Displacement • Velocity • Acceleration
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  Translational Motion: Moving ina Straight Line ● Occurs when an object moves in a straight line ● Described by linear quantities: ● Linear displacement ● Linear velocity ● Linear acceleration ● Example: A car moving down a highway
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  • Linear displacementis the change in position of an object along a straight path. Scenario: A car moves 100m in a straight line from Point A to Point B. Starting Point (A): 0 meters Ending Point (B): 100 meters Direction: East Linear Displacement = Final Position – Initial Position Ans.: Linear Displacement=100m−0m=100meters East Linear quantities: Displacement Δx: Δx=xf−xi where Δx is displacement, xf is the final position, and xi is the initial position.
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  • Linear velocity- how fast and in what direction an object is moving along a straight path. Linear quantities:
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  • Linear acceleration- measures how the linear velocity of an object changes with time. Linear quantities:
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  ROTATIONAL • Rotational motionhappens when an object spins around an axis. • The center point is called the axis of rotation. • “Turning or spinning around a center” EXAMPLES: • Electric fan • Ferris wheel • Spinning top • Bicycle wheel Angular Quantities • Angular displacement • Angular velocity • Angular acceleration
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  Angular Quantities
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  Linear Displacement vs. AngularDisplacement ● Linear Displacement: Total distance moved in a straight line ● Angular Displacement: Total angle rotated around an axis Compare and contrast
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  Angular displacement (θ)is the angle (in radians) through which an object moves on a circular path. One complete revolution around a circle equals 360 degrees, which is equivalent to 2𝜋 radian Angular displacement of a complete circle=2π radians or 360∘ Compare and contrast Angular displacement
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  Formula: θ =(Number of Rotations)(2π) Where: 𝜃= angular displacement (radians) 2𝜋radians = 1 complete rotation Angular Displacement Example: A Ferris wheel makes 4 complete rotations. Find its angular displacement. θ = n(2π) 𝜃 = 4 2𝜋 𝜃 = 8𝜋 radians
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  Linear Velocity vs.Angular Velocity ● Linear Velocity: Speed in a straight line ● Measured in meters per second (m/s) ● Angular Velocity: how fast something is rotating or spinning around a point or axis. Compare and contrast Formula:
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  Example: If a wheelspins 2 full circles in 4 seconds. Find the Velocity •One full circle = 2π radians •So, 2 full circles = 4π radians •Time = 4 seconds Angular Velocity Formula: 1 or π rad/ sec
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  Linear Acceleration vs.Angular Acceleration Linear Acceleration: Rate of change of linear velocity Angular Acceleration: Rate of change of angular velocity ● Both describe how quickly speed is changing Compare and contrast translational and rotational motion
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  Angular Acceleration Compare andcontrast translational and rotational motion
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  Example: If awheel’s angular velocity changes from 2π rad/s to 6π rad/s in 2 seconds. Find the angular acceleration. Compare and contrast translational and rotational motion Angular Acceleration 6π rad/s - 2π rad/s 2 seconds = 2 rad/s2 =
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  COMPARISON Translational Motion RotationalMotion Moves from one place to another Spins around an axis Uses linear quantities Uses angular quantities Example: moving car Example: spinning fan
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  • Both involvemovement. • Both can change speed. • Both are important in daily life. SIMILARITIES Remember!
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  ROLLING MOTION • Rollingobjects show two motions at the same time: • Translational Motion → moving forward • Rotational Motion → spinning around an axis Examples • Bicycle wheel • Toy car • Bowling ball Key Idea Objects like wheels and balls move and rotate simultaneously.
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  Main Linear Quantities •Displacement → distance moved • Velocity → speed with direction • Acceleration → change in speed Examples • Walking forward - Car moving on a road • Running athlete Linear quantities describe straight-line motion.
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  Main Angular Quantities •Angular displacement → amount of turning • Angular velocity → speed of rotation • Angular acceleration → change in rotational speed Examples • Spinning fan Ferris wheel Rotating gear Angular quantities describe rotational or circular motion.
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  Example Analysis In basketballshooting: • Arms rotate during the shot. • The player may jump forward translationally. • The ball rotates while moving through the air. Examples • Cycling Dancing • Basketball shooting Gymnastics Many physical activities combine translational and rotational motion.
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  APPLICATIONS IN REAL LIFE Linearand angular quantities are important in: • transportation • sports • machines • exercise SUMMARY EXAMPLES • Bicycle wheels rotate while moving forward. • Washing machines spin clothes. • Basketballs rotate while traveling. • Importance ⚬ Understanding motion helps: ￭ improve machine efficiency ￭ explain movement in everyday life ￭ understand sports performance