Rotational Motion
\nAn extended body is made up of several particles. However, if the particles remain constant the body is said to be rigid (Stanford and Tanner, 2014). The rotating particles do not change their energy of motion because the kinetic energy is dependent on mass and velocity. Rotational motion can, therefore, be described by other rotational variables.
\nThe rotational motion of a body is governed by the angular acceleration, the moment of inertia and the toque (Stanford and Tanner, 2014). The quantities are related such that if the angular acceleration is large for a long period of time t, then then the angular velocity and the rotation \u03b8 will be large. Therefore, the kinematics theory is used in describing the relationship between the quantities of rotational motion which include the rotational angle, the angular velocity, angular acceleration and time.
\nThe toque is the major contributing quantity in this experiment and therefore
\nToque \u03c4=r\u00d7F\u2026\u2026\u2026Eqn. 1
\nWhere r is the displacement between the line of action of force and the particle while F is the force applied
\nTherefore \u03c4=rFsin\u03b8\u2026\u2026\u2026.Eqn. 2, whereby \u03b8 is the angle between F and r
\nHowever from the second newton law of motion which states that F= ma where (F is the force applied and m is the mass while a is the acceleration), toque can be expressed as
\n\u03c4=mgrsin\u03b8\u2026\u2026\u2026\u2026\u2026\u2026Eqn. 3, where m is the mass and g is the acceleration due to gravity. Additionally, angular acceleration is another quantity that has a contribution from the experiment.
\n\u03b1=dw\/dt\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026Eqn. 4
\nFrom Newton\u2019s second law of motion;
\n\u03c4=I\u03b1\u2026\u2026\u2026\u2026..Eqn. 4, where \u03c4 is the applied torque, \u03b1 is the angular acceleration while I is the moment of inertia.
\nFrom the experiment, the tangential acceleration is represented by the following relationship.
\nI=mr^2 (g\/(\u221dr)-1)\u2026\u2026\u2026Eqn. 5, whereby g is the acceleration due to gravity while \u03b1 is the angular acceleration.<\/p>\n
Reference
\nStanford, A. L., & Tanner, J. M. (2014). Physics for students of science and engineering. Academic Press.<\/p>\n","protected":false},"excerpt":{"rendered":"
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