A fan blade rotates with angular velocity given by ωz(t)=ωz(t)= γγgamma −− ββbeta t2t2. a) Calculate the angular acceleration as a function of time. Express your answer in terms of the variables ββbeta, γγgamma, and ttt. b) If γγgamma_1 = 4.60 rad/srad/s and ββbeta_1 = 0.790 rad/s3rad/s3, calculate the instantaneous angular acceleration αzαz at ttt_0 = 3.00 ss. Express your answer in radians per second squared. c) If γγgamma_1 = 4.60 rad/srad/s and ββbeta_1 = 0.790 rad/s3rad/s3, calculate the average angular acceleration αav−zαav−z for the time interval tt = 0 to ttt_0 = 3.00 ss. Express your answer in radians per second squared.
A fan blade rotates with angular velocity given by ωz(t)=ωz(t)= γγgamma −− ββbeta t2t2. a) Calculate the angular acceleration as a function of time. Express your answer in terms of the variables ββbeta, γγgamma, and ttt. b) If γγgamma_1 = 4.60 rad/srad/s and ββbeta_1 = 0.790 rad/s3rad/s3, calculate the instantaneous angular acceleration αzαz at ttt_0 = 3.00 ss. Express your answer in radians per second squared. c) If γγgamma_1 = 4.60 rad/srad/s and ββbeta_1 = 0.790 rad/s3rad/s3, calculate the average angular acceleration αav−zαav−z for the time interval tt = 0 to ttt_0 = 3.00 ss. Express your answer in radians per second squared.
A fan blade rotates with angular velocity given by ωz(t)=ωz(t)= γγgamma −− ββbeta t2t2. a) Calculate the angular acceleration as a function of time. Express your answer in terms of the variables ββbeta, γγgamma, and ttt. b) If γγgamma_1 = 4.60 rad/srad/s and ββbeta_1 = 0.790 rad/s3rad/s3, calculate the instantaneous angular acceleration αzαz at ttt_0 = 3.00 ss. Express your answer in radians per second squared. c) If γγgamma_1 = 4.60 rad/srad/s and ββbeta_1 = 0.790 rad/s3rad/s3, calculate the average angular acceleration αav−zαav−z for the time interval tt = 0 to ttt_0 = 3.00 ss. Express your answer in radians per second squared.
A fan blade rotates with angular velocity given by ωz(t)=ωz(t)= γγgamma −− ββbeta t2t2.
a)
Calculate the angular acceleration as a function of time.
Express your answer in terms of the variables ββbeta, γγgamma, and ttt.
b)
If γγgamma_1 = 4.60 rad/srad/s and ββbeta_1 = 0.790 rad/s3rad/s3, calculate the instantaneous angular acceleration αzαz at ttt_0 = 3.00 ss.
Express your answer in radians per second squared.
c)
If γγgamma_1 = 4.60 rad/srad/s and ββbeta_1 = 0.790 rad/s3rad/s3, calculate the average angular acceleration αav−zαav−z for the time interval tt = 0 to ttt_0 = 3.00 ss.
Express your answer in radians per second squared.
Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .
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