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$\bullet$ When a toy car is rapidly scooted across the floor, it storesenergy in a flywheel. The car has mass $0.180 \mathrm{kg},$ and its fly-wheel has moment of inertia $4.00 \times 10^{-5} \mathrm{kg} \cdot \mathrm{m}^{2} .$ The car is15.0 $\mathrm{cm}$ long. An advertisement claims that the car can travel at a scale speed of up to 700 $\mathrm{km} / \mathrm{h}(440 \mathrm{mi} / \mathrm{h}) .$ The scalespeed is the speed of the toy car multiplied by the ratio of thelength of an actual car to the length of the toy. Assume a length of 3.0 $\mathrm{m}$ for a real car. (a) For a scale speed of $700 \mathrm{km} / \mathrm{h},$ what is the actual translational speed of the car?(b) If all the kinetic energy that is initially in the flywheel is converted to the translational kinetic energy of the toy, how much energy is originally stored in the flywheel? (c) What ini-tial angular velocity of the flywheel was needed to store theamount of energy calculated in part (b)?

a) 9.72 $\mathrm{m} / \mathrm{s}$b) 8.51 $\mathrm{J}$c) 652 $\mathrm{rad} / \mathrm{s}$

Physics 101 Mechanics

Chapter 9

Rotational Motion

Physics Basics

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

Hope College

University of Sheffield

McMaster University

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in the first part of this question, we're going to kill. Let the actual translation speed of the car that is we d over strike that relevant equation to solve this problem. We did the wanted by were Sequels, too lt divided by a let so called it acquired in one. Here we assist the velocity in scale. Lt is the length of the toy. And at least unless it's the Lindell the gun scared. Sorry, Len. Off the real car, not holding the square in for we d we can, right wit equals to lt you wanted by analysts. I want to play Weir's now setting the world is into this equation. We will get weed equals to 0.150 meter divided by 3.0 meter into 700 kilometer, but are so this will give us with vehicles too. 30.35 point zero kilometer. But so this is the answer off us part of this question. In second part of this question, we are going to complete that translation Kinetic energy bosses to buy the flyby that is get translation. Let me find a K A translation as translation equals to one by two and witty square. So call it equation too. Now setting the worries into equation too. We will get translation equals to one by two in tow 0.180 crazy in tow. 30 What? 5.0? Multiple opportunist part three meter divided by 3.6 month club return. It's part three seconds. Hold square Here We have converted the clue meters into meters and arson Two seconds. So this will give us translational equals to 8.50 Jules So this is the answer. The second part of this question In this part of the question, we have to conclude the angler velocity off the flyby, which is Omega in order to solve this problem. But we write the relevant equipment that is care. Rotational equals to one by two Iomega Square here at the moment off inertia the flywheel. So Soling the square for omega we will get my bike was two squared off. Two commendation rewarded by I. In this case, irritation equals two translation. While sitting the values into this equation we will get. My bike was two squared off to into 8.50 Joel divided by four born. 0012 Club attendance. Bottom on its wife. Good. You, me do a square. So this is me too square. No, This will give us my vehicles too. 652. Radiant. Farcical. So I know the question.

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