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1) a) An old wheat-grinding wheel in a museum actually works. The sign on the wall...

1) a)

An old wheat-grinding wheel in a museum actually works. The sign on the wall says that the wheel has a rotational acceleration of 190 rad/s^2 as its spinning rotational speed increases from zero to 1500 rpm.

How long does it take the wheel to attain this rotational speed?

Express your answer with the appropriate units.

1) b)

The speedometer on an automobile measures the rotational speed of the axle and converts that to a linear speed of the car, assuming the car has 0.62-m-diameter tires.

What is the rotational speed of the axle when the car is traveling at 22 m/s ?

Express your answer with the appropriate units.

1) c)

A string is wrapped around a uniform solid cylinder of radius r, as shown in (Figure 1). The cylinder can rotate freely about its axis. The loose end of the string is attached to a block. The block and cylinder each have mass m.

Find the magnitude α alpha of the angular acceleration of the cylinder as the block descends.

Express your answer in terms of the cylinder's radius r and the magnitude of the acceleration due to gravity g.

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