# Rotational Motion Formal Lab - Matt Darling Partner...

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Matt DarlingPartner: Muhammad AmjadTA: GettsLab section: 311/11/13Rotational Motion Formal LabThe motivation for this experiment was to explore the principles of rotational motion and to discern through experimentation if the equations that predict rotational motion based on Newtonian mechanics are accurate. The purpose of the experiment was to explore the concepts of angular kinematic variables, angular momentum, Newton’s second law for rotational motion, torque, and moments of inertia. Rotational kinematics is almost completely analogous to linear kinematics except the meaning of the variables is changed. Position is now measured in radians counterclockwise from the origin and is represented by theta. Velocity is now defined by dTheta/dT and is referred to by omega; the units for which are radians/s. Acceleration is now defined as dOmega/dt and is referred to by alpha; the units for which are radians/s/s. Force now referred to as torque and is the product of the moment of inertia and alpha. There also exists a simple connection between linear kinematics and rotational kinematics. Position = radius times theta. Velocity = radius times omega. Acceleration = radius times alpha. If the system is undergoing constant angular acceleration then it is similar to linear kinematics formulaically. so by subbing in the units they would become; ωf = ωo + αt and Θf = Θo +ωot + 1/2 αt^2. Torque can also be defined as F times L where F is force and L is the distance from axis of rotation. The direction of torque can be found from the cross product of the direction vector from the axis of rotation and the force vector. As hinted at previously newton’s second law is also applicable to rotational motion. In the equation F=MA force is replaced by the sum of the torque, mass is replaced by moment of inertia or I and a is replaced by alpha. The moment of inertia varies for all objects and depends on the shape as well as the axis of rotation. The moment of inertia is generally defined by the integral of P(r) r^2 Dv where P(r) is the objects mass density, r is position and Dv is volume. Angular momentum is the product of linear momentum and position however it can also be expressed in analogue to linear momentum with angular momentum (L) is equal to I times omega. The experiment had three parts. The first section dealt with the conservation of angular momentum in an inelastic collision. The system consisted of two metal plates.