Learning goal: to understand the definition and the meaning of moment of inertia; to be able to calculate the moments of inertia for a group of particles and for a continuous mass distribution with a high degree of symmetry. by now, you may be familiar with a set of equations describing rotational kinematics. one thing that you may have noticed was the similarity between translational and rotational formulas. such similarity also exists in dynamics and in the work-energy domain. for a particle of mass m moving at a constant speed v, the kinetic energy is given by the formula k=12mv2. if we consider instead a rigid object of mass m rotating at a constant angular speed ω, the kinetic energy of such an object cannot be found by using the formula k=12mv2 directly: different parts of the object have different linear speeds. however, they all have the same angular speed. it would be desirable to obtain a formula for kinetic energy of rotational motion that is similar to the one for translational motion; such a formula would include the term ω2 instead of v2. such a formula can, indeed, be written: for rotational motion of a system of small particles or for a rigid object with continuous mass distribution, the kinetic energy can be written as k=12iω2. here, i is called the moment of inertia of the object (or of the system of particles).

6–55 refrigerant-134a enters the condenser of a residential heat pump at 800 kpa and 358c at a rate of 0.018 kg/s and leaves at 800 kpa as a saturated liquid. if the compressor consumes 1.2 kw of power, determine (a) the cop of the heat pump and (b) the rate of heat absorption from the outside air.

You have been consulted by the mobile phone company hookup about a new augmented reality product called “brows”. they want to develop an alternative to google glasses, which, you recall, is a proposed new product which plans to superimpose a whole range of wireless google services over the user’s ordinary vision of the world. these appear in little circles and ovals, and let you phone people, take photographs, navigate across cities and inside buildings, find shops and update your social media. brows would do this too, but not be limited to special google services. the user would wear a small cylinder-shaped device designed to fit on top of their existing eyewear (glasses or sunglasses). it would project a reversed image onto the inside of the lenses, the reflection of which would be in focus for the user. instead of voice control, the user would control the device by eye and neck movements, which the device would track. the device would connect via bluetooth to the user’s phone, which would supply most of the computing power and wireless connectivity. hookup also wants to know what existing services would be most in demand, and which would not work well with brows. using your knowledge of augmented reality, wearable technology and interface design, is the project feasible? if not, why not? if feasible, how could the product need to be modified for a better experience?

Unpolarized light of intensity i_0=750w/m^2 is incident upon two polarizers. after passing through both polarizers the intensity is i_2=280w/m^2. (a) what is the intensity of the light after it passes through the first polarizer in w/m^2? (b) write an equation for the angle between the polarizers in terms of the initial (i_0) and final (i_2) intensities. (c) find the angle between the polarizers in degrees.