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A wheel 30 cm in diameter accelerates uniformly from 245 rpm to 380 rpm in 6.1 s . Part A How far will a point on the edge of the wheel have traveled in this time

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Answer:

A point on the edge of the wheel will travel 199.563 radians at the given time.

Explanation:

Given;

initial angular velocity of the wheel; [tex]\omega _i = 245 \ rev/\min = 245\ \frac{rev}{\min} \times \frac{2\pi}{1\ rev} \times \frac{1 \ \min}{60 \ s} = 25.66 \ rad/s[/tex]

final angular velocity of the wheel;

[tex]\omega _f = 380 \ rev/\min = 380 \ \frac{rev}{\min} \times \frac{2\pi}{1\ rev} \times \frac{1 \ \min}{60 \ s} = 39.80 \ rad/s[/tex]

radius of the wheel, d/2 = (30 cm ) / 2 = 15 cm = 0.15 m

time of motion, t = 6.1 s

The angular distance traveled by the edge of the wheel is calculated as;

[tex]\theta = (\frac{\omega_f + \omega_i}{2} )t\\\\\theta = (\frac{39.8 + 25.66}{2} )\times 6.1\\\\\theta = 199.653 \ radian[/tex]

Therefore, a point on the edge of the wheel will travel 199.563 radians at the given time.

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