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Odometer. The odometer (mileage gauge) of a car tells you the number of miles you have driven, but it doesn't count the miles directly. Instead, it counts the number of revolutionsof your car's wheels and converts this quantity to mileage, assuming a standard size tire and that your tires do not slip on the pavement. (a) A typical midsize car has tires 24 inches in diameter. How many revolutions of the wheels must the odometer count in order to show a mileage of 0.10 mile?(b) What will the odometer read when the tires have made $5,000$ revolutions? (c) Suppose you put oversize 28 -inch-diameter tires on your car. How many miles will you reallyhave driven when your odometer reads 500 miles?
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a) 84 revb) 5.95 milesc) 583 miles
Physics 101 Mechanics
Rotation of Rigid Bodies
Dynamics of Rotational Motion
Equilibrium and Elasticity
Simon Fraser University
University of Sheffield
In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.
In physics, rotational dynamics is the study of the kinematics and kinetics of rotational motion, the motion of rigid bodies, and the about axes of the body. It can be divided into the study of torque and the study of angular velocity.
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In the first part of this question, we are going to calculate the number of revolutions taken by the wheel that is theta in order to calculate this theta. Let me write. The equation is equal to r theta. Now call it equation 1. Solving this equation for theta. We can write theta equals to s divided by r, so call it equation. 2. Now setting the values into equation 2, we will get theta equals to 0.1 multiplied by 63360 inches divided by 12 inches. Here we have converted the miles into inches through this conversion. This will give us theta equals to 528 radiance or theta equals to 528 divided by 2 pi revolutions or theta equal to 84.0 revolutions. So this is the answer of first part of this question and second part of this question. We have to calculate the reading on the ordimeter of the car, which is as now setting the values into this equation. 1. We will get equal to 12 inches into 5000 revolutions or it can be written as x, equals to 12 by 63360 miles into 5000 multiplied by 2 pi radians. So this will give us s equals to 5.95 miles. Now, let's come toward the last part of this question this part of the question. We have to calculate that actually stance covered by the car, which is as now using the given values into equation 2. We will get theta equals to 500 multiplied by 63360 inches divided by 12 inch ont. So this will give us theta equals to 2.64 multiplied by 10. Is power 6 radiance now, given the now setting the values into equation? 1 of the previous light we can write is equals to 14 divided by 63360 miles, multiplied by 2.464, multiplied by 10 power 6 radiant. So this will give us equals to 583 miles so end of the question.
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