ppppp.pdf - Advanced Placement PHYSICS 1 Rotational Motion...

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Student 201 4 -201 5 PHYSICS 1 Rotational Motion Advanced Placement
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AP* is a trademark of the College Entrance Examination Board. The College Entrance Examination Board was not involved in the production of this material. Copyright © 2013 National Math + Science Initiative ® , Inc., Dallas, TX. All rights reserved. Rotational Motion What I Absolutely Have to Know to Survive the AP* Exam The rotational kinematic equations are rotational relationships between the angular displacement, angular velocity, angular acceleration, and time that are only true when the angular acceleration is constant (i.e. when the angular acceleration is not a function of θ as one example). There exists an almost perfect parallel between translational and rotational motion. In a system in which there is both rotation and translation, you must include both rotational and translational kinetic energy in the same conservation of energy expressions. Linear and Angular analogs - variables Linear Angular x Linear Distance (m) Rotational distance (radians) θ Δ x Linear Displacement (m) Rotational displacement (radians) Δθ v Linear Velocity (m/s) Rotational velocity (radians/s) ω a Linear Acceleration (m/s 2 ) Rotational acceleration (radians/s 2 ) α m Mass (kg) Rotational inertia (kg . m 2 ) Ι F Force (N) Torque (N . m) τ Rotational Inertia for a system of point masses = 2 mr I Σ = Rotational Inertia for common objects (not necessary to memorize) Solid Cylinder or Disc I = 1 2 mr 2 Hoop about center axis 2 mr I = Solid Sphere 2 5 2 mr I = Torque Just as a non-zero net force causes a linear acceleration, a non-zero net torque will cause an angular acceleration. A torque can be thought of as a twist, just as a force is a push or pull. It is a torque that affects an object’s angular velocity. Torque is not energy, however and the units are mN or N . m, not Joules. Torque = τ = r F = rF sin θ Where
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Copyright © 2013 National Math + Science Initiative ® , Inc., Dallas, TX. All rights reserved. Rotation I: Rotational Kinematics & Energy F = force that is being applied to object (N) r = displacement from the point of rotation to the point of force application (m) θ = angle between the force vector and the displacement vector Relationships between the linear and angular variables when an object is rotating around a fixed axis or rolling without slipping. Where r = the radius of the rotating object in meters a T = tangential acceleration in m/s 2 a C = centripetal acceleration (also called radial acceleration) in m/s 2 Key Formulas and Relationships Linear and Angular analogs – kinematics and energy equations Linear Angular Constant Motion x = x o + vt θ = θ o + ω t Motion with Constant Acceleration v = v o + at x = 1 2 ( v o + v ) t x = x o + v o t + 1 2 at 2 v o 2 = v 2 + 2 ax ω = ω o + α t θ = 1 2 ( ω o + ω ) t θ = θ o + ω o t + 1 2 α t 2 ω o 2 = ω 2 + 2 αθ 2 nd Law of Motion a = Σ F m = F net m α = Σ τ I = τ net I Kinetic Energy and Power Translational kinetic energy Rotational kinetic energy 2 2 1 mv K = 2 2
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