Physics Mechanics PHYS123
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This 2 page Class Notes was uploaded by Jasmine Ngo on Sunday March 27, 2016. The Class Notes belongs to PHYS123 at Illinois Institute of Technology taught by in Spring 2016. Since its upload, it has received 33 views. For similar materials see Mechanics in Physics 2 at Illinois Institute of Technology.
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Date Created: 03/27/16
Lecture: Rotational Motion, Torques, Moment of Inertia, and Newton’s 2nd Law of Rotation Constant angular acceleration equations: ω =ω0 +αt θ =θ0 +ωt + 1 /2 αt ^2 ω2 =ω0^ 2 + 2α(θ −θ0 ) This is analogous to kinematics equation where ω is in rad/s while α is in rad/s^2 Torque: τ = rFsinθ where force must be tangent to the object. Cross Product: The vector of torque can be found using the following: τ = r × F = rFsinθ where r and F are vectors and be solved by using cross product τ = r × F = (rx i + ry j + r z k)×(Fx i + Fy j + F z k) Kinetic Energy of Rotation: ∑ 1/2mv^2 Can also be written as KE = 1/ 2 Iω^2 where I is momentum of inertia Moment of Inertia: I=m1r ^2 +(2m2)r^2 where m1 is mass 1 and m2 is mass 2 Rotation about Center of Mass: Rotational intertia is given by I=m1r^ 2 + m2r^ 2 Moment of Inertia for Rod: 1 /3 mL^2 where L is the length of the rod. Parallel Axis Theorem: I = Icm+ mr^ 2 where Icm is the momentum of inertia of the center of mass It is important to note that rotation through the center of mass minimizes the moment of inertia Newton’s 2nd Law for Rotation: τ = Iα τ = rF For a pulley and tension string: τ = rFsin θ Inertial mass is how much force it takes to accelerate an object Rotational mass is how much torque it takes to accelerate an object. Rotational Power: τω