[HRW7 10.P.004.] The angular positionof a point on...

[HRW7 10.P.004.] The angular positionof a point on the rim of a rotating wheel is given by = 5.0t - 1.0t2 + t3,where is inradians and t is in seconds.
(a) What is the angular velocity at t =3 s?
rad/s
(b)What is the angular velocity at t = 5.0 s?
rad/s
(c) What is the average angular acceleration for the time intervalthat begins at t = 3 s and endsat t = 5.0 s?
rad/s2
(d) What is the instantaneous angular acceleration at the beginningof this time interval?
rad/s2
(e)What is the instantaneous angular acceleration at the end ofthis time interval?
rad/s2

Answers ( 1 )

  1. maélie perez
    maélie perez
    You just need to differentiate q(t) to the angular velocity andangular acceleration
    q'(t) = 5 -2t+3t2
    q'' (t) =-2 +6t
    Then plug in the values of t.
    (a) t = 3 => 26 rad/sec
    (b) t = 5 => 70 rad/sec
    (c) angular acc. at t = 3 is

    -2 +6(3) = 16 rad/sec2
    angular acc. at t = 5 is

    -2 +6(5) = 28 rad/sec2
    The average is (28 + 16) /2 = 22rad/sec2
    (d) and (e)..see (c) above

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