An automobile engine can produce 200 N · m of torque. Calculate the angular acce

Question

An automobile engine can produce 200 N · m of torque. Calculate the angular acceleration produced if 95.0% of this torque is applied to the drive shaft, axle, and rear wheels of a car, given the following information. The car is suspended so that the wheels can turn freely. Each wheel acts like a 15.0 kg disk that has a 0.180 m radius. The walls of each tire act like a 2.00-kg annular ring that has inside radius of 0.180 m and outside radius of 0.320 m. The tread of each tire acts like a 10.0-kg hoop of radius 0.330 m. The 14.0-kg axle acts like a rod that has a 2.00-cm radius. The 30.0-kg drive shaft acts like a rod that has a 3.20-cm radiu

Explanation / Answer

Torque applied on rear wheels, T = 0.95*200 = 190 N.m


for annular ring, I = m*(r1^2+r2^2)/2

moemnt of inertia of rear wheels, I1 = 2*m*(r1^2+r2^2)/2

I2 = 2*(0.18^2+0.32^2) = 0.2696 kg.m^2

moment of if inertai of cyllinder or rod = m*r^2

I2 = 14*0.032^2 = 0.014336 kg.m^2

I = I1+I2 = 0.283936 kg.m^2


we know, T = I*alfa

==> alfa = T/I = 190/0.283936 = 669 rad/s^2

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