A disk 7.90 cm in radius rotates at a constant rate of 1 190 rev/min about its central axis. (a) Determine its angular speed. 124.58 Correct

Question

A disk 7.90 cm in radius rotates at a constant rate of 1 190 rev/min about its central axis. (a) Determine its angular speed. 124.58 Correct: Your answer is correct. rad/s (b) Determine the tangential speed at a point 2.98 cm from its center. 3.71 Correct: Your answer is correct. m/s (c) Determine the radial acceleration of a point on the rim. magnitude 1.23 Correct: Your answer is correct. km/s2 direction toward the center Correct: Your answer is correct. (d) Determine the total distance a point on the rim moves in 2.06 s. 20.28 Correct: Your answer is correct. m

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Dulcie 4 years 2021-09-05T10:55:38+00:00 1 Answers 37 views 0

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  1. thienthanh
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    2021-09-05T10:56:43+00:00
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    Answer:

    124.62\ \text{rad/s}

    3.71\ \text{m/s}

    1.23\ \text{km/s}^2

    20.28\ \text{m}

    Explanation:

    r = Radius of disk = 7.9 cm

    N = Number of revolution per minute = 1190 rev/minute

    Angular speed is given by

    \omega=N\dfrac{2\pi}{60}\\\Rightarrow \omega=1190\times \dfrac{2\pi}{60}\\\Rightarrow \omega=124.62\ \text{rad/s}

    The angular speed is 124.62\ \text{rad/s}

    r = 2.98 cm

    Tangential speed is given by

    v=r\omega\\\Rightarrow v=2.98\times 10^{-2}\times 124.62\\\Rightarrow v=3.71\ \text{m/s}

    Tangential speed at the required point is 3.71\ \text{m/s}

    Radial acceleration is given by

    a=\omega^2r\\\Rightarrow a=124.62^2\times 7.9\times 10^{-2}\\\Rightarrow a=1226.88\approx 1.23\ \text{km/s}^2

    The radial acceleration is 1.23\ \text{km/s}^2.

    t = Time = 2.06 s

    Distance traveled is given by

    d=vt\\\Rightarrow d=\omega rt\\\Rightarrow d=124.62\times 7.9\times 10^{-2}\times 2.06\\\Rightarrow d=20.28\ \text{m}

    The total distance a point on the rim moves in the required time is 20.28\ \text{m}.

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