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Rotational-Motion the solution to the system
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- 3. 3 Rotational Motion- ByAditya Abeysinghe Definitions of some special terms 1. Angular position (Φ) - The angular position of a particle is the angle made between the line connecting the particle to the ɸ original and the positive direction of the x-axis, measured in a counterclockwise direction 2. Angular displacement (θ) - The radian value of the angle displaced by an object on the center of its path in circular motion from the initial position to the final position is called the angular displacement. = ɸ l / r
- 4. 4 3. Angular Velocity(ω)- Angular velocity of an object in circular motion is the rate of change of angular displacement over time Rotational Motion- By Aditya Abeysinghe θ = θf - θi ω = θ / t Unit - rads-1 Vector direction by Right hand rule
- 5. 5 Rotational Motion- ByAditya Abeysinghe 4. Angular acceleration- Angular acceleration of an object in circular motion is the rate of change of angular velocity over time θ ω ω0 r t = 0 t = t α = (ω – ω0) / t Unit- rads-2 Direction- By right hand rule
- 6. 6 Rotational Motion- ByAditya Abeysinghe Angular equations of movement α = (ω – ω0) / t ω = ω0 + αt (ω + ω0 )/2 = θ / t θ = (ω + ω0 )t/2 (ω + ω0 )/2 = θ / t , ωt = 2θ + ω0t , (ω0 + αt)t = 2θ + ω0t θ = ω0t + ½ αt2 θ = (ω + ω0 )t/2, θ = (ω + ω0 )(ω - ω0 ) 2 α ω2 = ω0 2 + 2αθ
- 7. 7 Therefore the fourequations of angular movement are- 1. ω = ω0 + αt 2. θ = (ω + ω0 )t/2 3. θ = ω0t + ½ αt2 4. ω2 = ω0 2 + 2αθ It should be noted that these four equations are analogous to the four linear equations of motion: 5. V = U + at 6. S = (V + U)t/2 7. S = Ut + ½ at2 8. V2 = U2 + 2as Where: V: Final velocity U: Initial velocity a: Acceleration t: Time S: Displacement (change in position)
- 8. 8 Rotational Motion- ByAditya Abeysinghe Displacement Velocity Acceleratiom Translational motion S V a Rotational motion θ ω Α
- 9. 9 Rotational Motion- ByAditya Abeysinghe TORQUE Torque is called the moment of force and is a measure of the turning effect of the force about a given axis. A torque is needed to rotate an object at rest or to change the rotational mode of an object. The rate of change of angular momentum of an object in rotational motion is proportional to the external unbalanced torque. The direction of the torque also lies in the direction of the angular momentum.
- 10. 10 Rotational Motion- ByAditya Abeysinghe ROLLING BODY Rolling is a combination of rotational and transitional(linear) motions. Suppose a sphere is rolling on a plane surface, the velocity distribution can be expressed as,
- 11. 11 Rotational Motion- ByAditya Abeysinghe Summarizing it up! Term Definition Angular position The angular position of a particle is the angle made ɸ between the line connecting the particle to the original and the positive direction of the x-axis, measured in a counterclockwise direction Angular displacement The radian value of the angle displaced by an object on the center of its path in circular motion from the initial position to the final position is called the angular displacement. Angular velocity Angular velocity of an object in circular motion is the rate of change of angular displacement Angular acceleration Angular acceleration of an object in circular motion is the rate of change of angular velocity Torque Torque is called the moment of force and is a measure of the turning effect of the force about a given axis.
- 12. 12 Rotational Motion- ByAditya Abeysinghe TRANSLATIONAL MOTION ROTATIONAL MOTION Points have equal linear displacement Points have varying linear displacements Points travel in the same direction Points travel in varying directions Points travel with the same linear velocity Points travel with different linear velocities Points travel with the same linear acceleration Points travel with varying linear accelerations Linear displacement Angular displacement Linear velocity Angular velocity Linear acceleration Angular acceleration
- 13. DANCE/EXERCISE ROUTINE 1. Activity:The teacher groups the learners into groups with a maximum of five members. The teacher instructs the learners to design a two- to three- minute dance or exercise routine exemplifying translational and rotational motion through body movement. The routine may or may not have musical accompaniment. For every movement, the performers will state whether the action demonstrates translational motion or rotational motion by saying “translational” or “rotational.” 2. The routine will be presented on the next meeting. 3. After all groups have presented, the teacher asks the question: How important is understanding translational and rotational motion in human movement? 4. The teacher summarizes the discussion, focusing on the application of translational and rotational motion in human movement. RUBRIC: conceptual accuracy (25%), creativity and originality (20%), execution and coordination (20%), scientific integration and explanation (20%), and presentation and engagement (15%).