Theory of Machines - 1 - Mechanical Engineering (MCQ) questions and answers for Q. 4426

Q.  Calculate the angular speed of driven shaft if the driving shaft has angular speed of 400 rpm. When shaft angle is 20o and angle of rotation is 40o in Hooke's joint.
- Published on 06 Aug 15

a. 40.23 rad/s
b. 42.45 rad/s
c. 36.82 rad/s
d. None of the above

ANSWER: 42.45 rad/s

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    Discussion

  • Sravanthi   -Posted on 21 Oct 15
    Given: Angular speed of driving shaft = 400 rpm, shaft angle (α) = 20°, angle of rotation (θ) = 40°

    Formula: Angular speed of driven shaft (ω2) = (ω1 cos α) / (1- cos2 θ sin2 α)

    Solution:

    Angular speed of driving shaft ( ω1 ) = (2 π N) / 60 = (2 x π x 400) / 60

    = 41.88 rad /s


    Therefore angular speed is calculated by substituting the given values,

    Angular speed of driven shaft (ω2) = (ω1 cos α) / (1- cos2 θ sin2 α)

    = (41.88 x cos 20°) / (1 – cos2 40 x sin2 20)

    = 42.45 rad /s

    The angular speed of driven shaft is 42.45 rad / s when the driving shaft has angular speed of 400 rpm.

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