Please draw diagram and show work for A-D. 9.1 Angular Velocity and Acceleration
ID: 1779995 • Letter: P
Question
Please draw diagram and show work for A-D. 9.1 Angular Velocity and Acceleration . A 25 kg child is pushing a merry-go-round. The angle through which the merry-go-round has turned varies with time according to the following equation: (t) = Yt + , where Y is 0.40 rad/s and is 0.012 rad/s3. (a) Calculate the angular velocity of this merry-go-round. (b) What is the initial value of the angular velocity? (c) calculate the instantaneous value of the angular velocity at 5 seconds, the average value of the angular velocity (from 0 to 5). (d) Show that the average angular velocity is not equal to the average of the instantaneous angular velocities for t = 0s and t =5s.Explanation / Answer
Given,
theta(t) = gamma t + beta t^3
gamma = 0.4 rad/s ; beta = 0.012
theta = 0.4 t + 0.012 t^3
a)we know from the defination of angular velocity
w = d(theta)/dt
w = d(0.4 t + 0.012 t^3)/dt = d(gamma t + beta t^3)/dt
w = gamma + 3 beta t^2
w = 0.4 + 3 x 0.012 t^2 = 0.4 + 0.036 t^2
w = 0.4 + 0.036 t^2
Hence, w = 0.4 + 0.036 t^2 ; w = gamma + 3 beta t^2
b)for t = 0
w = gamma = 0.4 rad/s
c)t = 5
w = 0.4 + 0.036 x 5^2 = 1.3 rad/s
Hence, w = 1.3 rad/s
avearge is: w(av) = (0.4 + 1.3)/2 = 0.85 rad/s
Hence, w(avg) = 0.85 rad/s
d)avg angular velocity is:
w(avg) = 0.4 rad/s
w(0-5) = 0.85 rad/s
Hence, the above two values are not equal.