Physics Week 10 Notes
Physics Week 10 Notes PHYS2001
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This 6 page Class Notes was uploaded by Grace Lillie on Monday March 28, 2016. The Class Notes belongs to PHYS2001 at University of Cincinnati taught by Alexandru Maries in Fall 2016. Since its upload, it has received 27 views. For similar materials see College Physics 1 (Calculus-based) in Physics 2 at University of Cincinnati.
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Date Created: 03/28/16
Chapter 11 – Angular Momentum 11.1 – The Vector Product and Torque vector product (cross product): , and the magnitude is τ=rFsinθ - use the right-hand rule to determine direction: extend fingers along r and curl them in the direction of F. The direction of you thumb is the direction of the vector product. - the vector product is not commutative: the order matters! 11.2 – Analysis Model: Nonisolated System (Angular Momentum) - torque plays the same role in rotational motion that force plays in translational motion L=⃗r×p - Angular momentum: the cross product of position and linear momentum d L dp⃗ ∑ τ= compare to: ∑ F= dt dt Torque changes angular momentum like force changes linear momentum *the same axis must be used to measure both angular momentum and torque *the SI unit for angular momentum is kg·m /s *using right hand rule, angular momentum is perpendicular to linear momentum and position vectors L=mvr sinφ magnitude of angular momentum. φ is the angle between r and p ⃗ τ = d Ltot For a system of particles: ext dt angular impulse-angular momentum theorem 11.3 – Angular Momentum of a Rotating Rigid Object L=Iω magnitude of angular momentum. It is in the same direction as angular velocity ∑ ⃗extα Rotational form of Newton’s second law 11.4 – Analysis Model: Isolated System (Angular Momentum) In an isolated system, angular momentum is conserved: , Iiωi=I f f 11.5 – The Motion of Gyroscopes and Tops precessional motion – the motion of the symmetry axis around the vertical axis precessional frequency – the angular speed of the axle about the vertical axis Chapter 12 – Static Equilibrium and Elasticity 12.1 – Analysis Model: Rigid Object in Equilibrium rigid object in equilibrium: both net external force and net external torque must be zero - translational equilibrium (translational acceleration of center of mass is zero) - rotational equilibrium (angular acceleration about any axis must be zero) static equilibrium: the object is at rest relative to the observer (no translational or angular speed) 12.2 – More on the Center of Gravity The center of gravity is located at the center of mass only if gravitational acceleration is uniform over the entire object. Otherwise: 12.3 – Examples of Rigid Objects in Static Equilibrium Net external torque is zero when the center of gravity is directly over the support point 12.4 – Elastic Properties of Solids stress—the external force acting on an object per unit cross-sectional area strain—the result of stress; a measure of the degree of deformation stress elastic modulus—a proportionality constant, equal to the ratio: strain - Young’s modulus measures resistance of a solid to change in length - Shear modulus measures resistance to motion of parallel planes within a solid - Bulk modulus measures resistance of solids/liquids to changes in volume Young’s Modulus: Elasticity in Length tensile stress—the ratio of the magnitude of the external force F to cross-sectional area A, where the cross section and force vector are perpendicular tensile strain—the ratio of change in length to original length. a dimensionless quantity Y≡ tensile str=ssF/ A tensilestrain∆L/L i units are force per unit area elastic limit—the maximum stress that can be applied before it becomes permanently deformed Shear Modulus: Elasticity of Shape The force applied is parallel to one of the object’s faces while the opposite face is held fixed shear stress—ratio of tangential force to area of the face being sheared shear strain—ratio of horizontal distance the sheared face moves to the object’s height shear stress F /A S≡ = shear strain ∆ x/h Bulk Modulus: Volume Elasticity response of object to changes in a force of uniform magnitude applied over the entire surface of an object, such as when an object is submerged in a fluid. Results in change in volume, not shape volume stress—ratio of magnitude of the total force to the area of the surface pressure—P=F/A volume strain—the change in volume divided by the initial volume B≡ volumestress= −∆F /A = −∆ P volumestrain ∆V /Vi ∆V /Vi *the negative sign is so that B is a positive number. (Increase in pressure causes decrease in volume) compressibility—the reciprocal of the bulk modulus Prestressed Concrete the maximum stress before fracture occurs depends on the nature of the material and the type of applied stress Concrete is much stronger under compression than tension or shear, so vertical columns can support more than horizontal beams. Steel rods reinforce concrete. Steel rods under tension as concrete is being poured, then released after the concrete cures, results in permanent tension in the steel and compressive stress on the concrete, allowing the slab to support a much heavier load.
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