A disk 7.98 cm in radius rotates at a constant rate of 1 250 rev/min about its central axis. (a) Determine its angular speed. rad/s (b) Determine the tangential speed at a point 3.10 cm from its center. m/s (c) Determine the radial acceleration of a point on the rim. magnitude km/s2 direction (d) Determine the total distance a point on the rim moves in 1.90 s. m


  1. Answer with Explanation:

    We are given that

    Radius of disk=r=7.98 cm=0.0798 m

    1 m=100 cm

    a.Angular speed=1250rev/min

    2\pi rad=1 rev

    1250 rev/min=1250\times 2\pi rad/min

    1 min=60 sec

    Angular speed=\omega=\frac{1250\times 2\pi}{60} rad/s

    Angular speed=\omega=130.9 rad/sec

    b.r=3.1 cm=\frac{3.1}{100}=0.031m

    1 m=100 cm

    v=r\omega=0.031\times 130.9=4.058m/s

    Hence, the tangential speed=4.058m/s

    c.Radial acceleration=a=r\omega^2=(130.9)^2(0.0798)=1367.36m/s^2

    Hence, the radial acceleration of a point on the rim=1367.36 m/s^2

    d.Time, t=1.9 s

    Total distance=d=r\omega t

    d=0.0798\times 130.9\times 1.9

    d=19.8 m

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