Phys 201 1nd Edition Lecture 20 Outline of Last Lecture I. Torque and angular accelerationOutline of Current Lecture II. ImpulseIII. Angular vs. Linear MomentumIV. InertiaA. Inertia for different objectsB. Inertia and torqueCurrent LectureImpulse:When one object strikes another object in a collision, there is a period of time, though usually very small, in which that object enacts a certain amount of force on the other. The measure of this force in this period of time is an impulse. The because an impulse is equal to force(N) times time(s), the units for the impulse are Ns. However, the units for impulse can also be representedas kg m/s. Equationally, the impulse(J) is represented as;J=FΔtThe impulse of a force in a given time period is equal to the change in the linear momentum produced over this same time period. Remember that the basic equation for momentum(p) is;Δp=mVTherefore, the equations for impulse and change in momentum can be combined to fine the connection between impulse and mass and/or velocity.J=Δp FΔt=mVAngular vs. Linear Momentum:These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.Linear momentum refers to an object of a mass (m) moving in a straight line with a velocity (V). Angular momentum, on the other hand, refers to an object with a mass (m) rotating around a circle with a radius (R) at a certain angular velocity (ω) measured in radians/second. The equation for angular momentum (L) is then;L=mR2ωBecause angular velocity is simply velocity/radius, this equation can be simplified to;L=mR2(V/R) L=mRVThis means that the angular velocity of an object is equal to its linear velocity, times the radius of its circular path.Inertia:More often than the above equation, you will see angular velocity written as a product of the objects moment of inertia (I) and its angular velocity. The moment of inertia is calculated as mR2, which makes the more common equation for angular momentum;L=IωFor large rotating objects (instead of a system of smaller objects), the moment of inertia can be calculated with a single equation. However, the moment of inertia differs depending on the typeand shape of the object. The most common objects and the equations for their moment of inertia are in the table below.Shape EquationHoop or Hollow Cylinder I=mR2Disk I=.5mR2Sphere I=(2/5)mR2Center of rotating rod I=(1/12)mL2Torque and Inertia:Angular momentum is a vector with directionality and magnitude. The direction of the angular momentum is the same as that of the angular velocity. Angular momentum is generated or absorbed by the application of torques, correlating with Newton’s law of inertia. In other words,to cause an object to rotate you must create angular momentum. To stop an object from rotating you must absorb its angular momentum. To do either, you must change the inertia of the rotating object by applying torque. Because the amount of torque applied to an object affects the inertia and angular acceleration of the object, the product of the moment of inertia and acceleration will be equal to the net torque on the object. Therefore, the equation for torque of rotation
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