( a ) What is the least time required for the rotation? (b) What is the correspo
ID: 1291066 • Letter: #
Question
(a) What is the least time required for the rotation?
(b)What is the corresponding value of ?1?
(a) The angular velocity (rad/s)
(b) The angular position (rad) as functions of time (s).
A disk, with a radius of 0.25 m, is to be rotated like a merry-go-round through 800 rad, starting from rest, gaining angular speed at the constant rate- alpha 1 through the first 400 rad and then losing angular speed at the constant rate - alpha 1 until it is again at rest. The magnitude of the centripetal acceleration of any portion of the disk is not to exceed 400 m/s^2. (a) What is the least time required for the rotation? (b)What is the corresponding value of ?1? The angular acceleration of a wheel is alpha = 6.0t^4 -4.0 t^2 with Alpha 6.0t4- 4.0t2, with alpha in radians per second-squared and t in seconds. At time t = 0, the wheel has an angular velocity of +2 rad/s and an angular position of +1 rad. Write expressions for: (a) The angular velocity (rad/s) (b) The angular position (rad) as functions of time (s).Explanation / Answer
a = r*w^2 = 400
w^2 = (400)/(0.25)
w = 40 rad/s
theta 1= 400 = (40+0)/2*t1
t1 = 20 s
theta 2 = 400 = (40+0)/2*t2
t2 20 s
a) T = t1 + t2 = 80s
b) alfa = w/t1 = 40/20 = 2 rad/s^2
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a) w = 6t^5/5 - 4t^3/3 + wo
w = 6t^5/5 - 4t^3/3 + 2
b) angular position = theta = t^6/5 - t^4/3 + wo*t + thetao
theta = = t^6/5 - t^4/3 + 2*t + 1
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