Mei-Ting SongLab Partner: Ryan PerryZachary ButlerSection 611/12/2015Rotational Motion Lab ReportIntroductionThe purpose of this lab is to study rotational motion in a closed system. Angular qualities are used to describe rotational kinematics and dynamics; it is very closely related to linear kinematics and dynamics. The angular displacement is the defined as the angle at which an object turns. A positive displace will rotate counter clockwise where as a negative displace will rotate clockwise. The units for displacement are radians which are dimensionless. The equation to solve a radian is the arc length divided by the radius (θ=sr). Since one rotation around the circle is 2πr there are 2π radians in 360˚. When you take the derivative of the angular displacement, you get the rate of change of the angle with respect to time. This quantity is called angular velocity and is represented using the symbol omega, ω. The units of angular velocity are s-1 which is radians per second however radians again are dimensionless. If you take the derivative of angular velocity you get angular acceleration which is represented using alpha, α. Again its units will be s-2 because it is radians per second squared but radians are dimensionless. There is a direction correlation between linear and angular quantities. Where s=rθ, v=rω and a=rα. Therefore, if there is a constant acceleration the equation in linear kinematics can be used for rotational kinematics. However, position will be replaced with angle, velocity is replaced with angular velocity and constant acceleration is replaces with constant angular acceleration. Thus the new equations will be ωf=ωo+αtand θf=θo+¿ωot12α t2.Torque is basically rotational force and can be solved by multiplying the magnitude of theforce by lever arm. Torque is positive when it is rotating counter clockwise and negative when it

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is rotating clockwise i.e. right hand rule. The general definition of torque can be found by the cross product of the position vector and the force. Newton’s 2ndlaw still holds true for rotational motion. However, linear motion must be replaced with moment of inertia. Therefore the equation is ∑τ=Iαwhere I is the moment of inertia (kg m2 ) and α is the angular acceleration. The moment of inertia is found fromintegrating the product of the mass density, position squared, and volume element. Therefore, I isproportional to the mass. In our experiment, we need the moment of inertia for a disk which is12mr2where m is the mass and r is the radius of rotation. The last concept we learned and observe in this lab is angular momentum. It is depicted as ⃗Land is found by multiplying the position vector by the linear momentum. Therefore,⃗L=⃗r x⃗pis the equation described. Angular momentum can also be written as L=Iω where I isthe moment of inertia and ω is the angular momentum.Materials3 disks (2 steel and one aluminum)RulerAir pumpRotational motion apparatus File given by instructorDataStudioAir vent drop pin