Please include units with all your calculations, otherwise I won\'t be able to u

Question

Please include units with all your calculations, otherwise I won't be able to understand your work. Thanks!

CP1: The angular position function of a particle is given by: theta=At+Bt^2+Ct^4 where A=8.5rad/s, B= - 15.0 rad/s^2, C= 1.6rad/s^4 a. Derive the angular velocity and angular acceleration functions b. Find the instantaneous angular acceleration at t=2.0s c. Find the average angular acceleration between t=1.0s and t=3.0s d. Find the instantaneous angular velocity at t=2.0s e. Find the average angular velocity between t=1.0s and t=3.0s

Explanation / Answer

a)

W = d(theta)/dt = A + 2Bt + 4Ct^3 = 8.5 - 30t + 6.4t^3

angular acc = dW/dt = -30 + 19.2t^2

b)

angular acc at t = 2 sec

= -30 + 19.2*(2)^2 = 46.8 rad/s^2

c) avg acc = W2-W1/(t2-t1) =  8.5 - 30*3 + 6.4*3^3 - (  8.5 - 30*1 + 6.4*1^3) /(3-1) = 53.2 rad/s^2

d) W =  8.5 - 30t + 6.4t^3 , at t=2 W = 8.5 - 30*2 + 6.4*2^3 = -0.3 rad/s

e) avg angular velocity = theta2 - theta1/(t2-t1) = 8.5*3 - 15*(3)^2 + 1.6*(3)^4 - (8.5*1 - 15*(1)^2 + 1.6*(1)^4) /( 3-1)

= 12.5 rad/s

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