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16. Problem 12.6E (HRW) An automobile has a total of mass of 1700 kg. It accelerates from rest to 40 km / h in 10 s. Assume each wheel is a uniform 32 kg disk. Find, for the end of the 10 s interval, (a) the rotational kinetic energy of each wheel about its axle, (b) the total kinetic energy of each wheel, and (c) the total kinetic energy of the automobile. |
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Solution: Click For PDF Version (a) Let m be the mass and r be the radius of each
wheel. Assuming that each wheel is a uniform disk, the rotational inertia of
each wheel will be given by the expression
As the car is moving normally that is without slipping the angular speed of each wheel will be
The rotational kinetic energy of each wheel will, therefore, be
(b) As the centre of mass of each wheel is moving with speed v, the kinetic energy of translation of each wheel will be
The total kinetic energy of each wheel will be
(c) The total kinetic energy of the automobile will be the sum of the translational kinetic energy of the automobile and the rotational kinetic energy of the 4 wheels. Therefore,
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Let v
be the speed of the car after 10 s starting from rest.
