Phys 201 1nd Edition Lecture 22 Outline of Last Lecture I. Angular momentum and rotational kinetic energyOutline of Current Lecture II. ReviewA. PowerB. ImpulseC. MomentumD. Gravitational Potential EnergyE. TorqueF. Rotational Kinetic EnergyCurrent LecturePower:Power describes the speed at which work is done. Power can be described/calculated from the following equations; P=ΔW/Δt  P=FΔX/Δt  P=FV Where W represents work, t represents time, x represents distance and V represent velocity.Because power is energy over time, the unit for power is J/s, which are also called Watts. Most objects can only put out a limited amount of power. This means that if a person continues to increase the force they are applying to something, they will have to adjust their speed in order to stay within the parameters of their available power (e.g. when riding a bike up a hill, you have to pedal slower when youuse more work to keep moving up).Impulse:The impulse helps relate actual force of a system to the average force. The most common example of an impulse is in the case of a collision in which an “equal and opposite” force is experienced for a certain amount of time, causing the momentum of the object to change. This force in this amount of time experienced is the impulse, and it is equal to the momentum of the object.Conservation of 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.Momentum is used to describe a change in motion of an object. The momentum (p) of a force is calculated by multiplying mass by velocity, where momentum and velocity are both vectors. If two objects collide with one another and the momentum lost by one object will be equal to the momentum gained by the other object, then there is no change in in the momentum over time, meaning that the final and initial momentums are the same. This is called conservative momentum. For objects with the same momentum, the object with the fastest speed will have the greatest kinetic energy. If one car collides with another car, the most damage will come from (meaning that the most energy will be lost) when it collides with an object of the greatest velocity, even if it has a smaller mass. Conservative momentum is calculated from the equation; m1V1+m2V2=m1V1’+m2V2’ in which the superscript (‘) indicates that we are looking at the final velocity after the collision, when the objects are moving away from each other. The velocities without a superscript indicate the initial velocity before the collision, when the objects are moving towards each other.Inelastic collisions conserve momentum, but not kinetic energy. An elastic collision, on the other hand, isone in which both momentum and kinetic energy are conserved throughout the collision.Gravitational potential energy:Gravity is related to the height of an object. Gravitational potential energy (PE=mgh) depends on h, which is based on a subjective reference point and assumes that a constant force is used to lift something to any given height. However, because this is inaccurate and force does change with distance, a more accurate measurement for the force of gravity is the equation Newton’s universal law of gravitation;F=(mMeG)/R2 Where m is the mass of the object, Me is the mass of Earth, G is the gravitational constant, and R is the radius of the object in relation to the center of the Earth. However, an object changes potential energy as it moves, considering its change in position. This means that the radius(R) is not constant meaning that a more apt equation would be;ΔPE=-GmM(1/rf - 1/ri)Rotational Motion:Rotational motion differs only slightly from linear motion. We describe a rotating object in terms of angular acceleration (α), which is just the change in (ω) angular velocity (ω) over the change in time. LinearMotionRotatingMotion x θ V ω a αx=x0+Vit + .5at2  θ=θ0+ω0t+.5αt2V=V0+at  ω=ω0+αtV2=V02+2a(x-x0)  ω2=ω02+2α(θ-θ0)Torque:Torque is as a measure of how much the force acting on an object can change the motion of the object. The simplest equation for torque(T) is T=rF, where r is the distance from pivot point that the force (F) is acting on the object. For torque to work, r and F must be perpendicular to one another. The perpendicular position of these two vectors is called the lever arm. If the force is working on the object at an angle, the torque is measured as T=rFsin(θ). The moment of inertia (Tnet=Iα) determines the amount of torque required to rotate an object about an axis with a certain angular acceleration. The moment of inertia depends on the mass of an object and the distribution of that mass. Rotational kinetic energy:Linear kinetic energy (KE) is equal to .5 time the mass (m) of the object times the square of the velocity (V). Rotational kinetic energy is similar, except we use the moment of inertia (I) instead of mass, and the angular velocity (ω) instead of velocity. KE(linear)=.5mV2KE(rotational)=.5Iω2Some rotating objects have both linear and rotational kinetic energy. If you roll a ball across a surface theball has rotational movement where it is spinning around its axis and linear movement as it moves acrossthe ground. To calculate the total kinetic energy of the ball, both the rotational and linear kinetic energy need to be taken into consideration. This means that;KEtotal=KErotational + KElinear  KEtotal=(.5)Iω2 +