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Posted: October 15th, 2022
Rotational Motion
Rotational Motion
An 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.
The 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 θ 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.
The toque is the major contributing quantity in this experiment and therefore
Toque τ=r×F………Eqn. 1
Where r is the displacement between the line of action of force and the particle while F is the force applied
Therefore τ=rFsinθ……….Eqn. 2, whereby θ is the angle between F and r
However 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
τ=mgrsinθ………………Eqn. 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.
α=dw/dt……………………Eqn. 4
From Newton’s second law of motion;
τ=Iα…………..Eqn. 4, where τ is the applied torque, α is the angular acceleration while I is the moment of inertia.
From the experiment, the tangential acceleration is represented by the following relationship.
I=mr^2 (g/(∝r)-1)………Eqn. 5, whereby g is the acceleration due to gravity while α is the angular acceleration.
Reference
Stanford, A. L., & Tanner, J. M. (2014). Physics for students of science and engineering. Academic Press.
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