A uniform solid disk with radius 10 cm has mass 0.8 kg (moment of inertia I = (1
ID: 1454901 • Letter: A
Question
A uniform solid disk with radius 10 cm has mass 0.8 kg (moment of inertia I = (1/2)MR2). A constant force 12 N is applied as shown. At the instant shown, the amount of string that has wound off the disk is d =30 cm, and the angular velocity of the disk is 45 radians/s into the page.
(a) At this instant, what are the magnitude and direction of the angular momentum about the center of the disk?
_____ kg·m2/s
(b) At a time 0.3 s later, what are the magnitude and direction of the angular momentum about the center of the disk?
_____ kg·m2/s
(c) At this later time, what are the magnitude and direction of the angular velocity of the disk?
_____ rad/s
Explanation / Answer
torque = I x alpha
12x0.1 = 0.004 x alpha
alpha = 300 rad/sec^2
a)
angular momentuym
L = I w
L = MR^2/2 w
L = 0.18 kg·m2/s
b)
torque x time = change in angular momentum
t = w/alpha + 0.3
t = 0.15 + 0.3
t = 0.45 sec
angular momentum
L = 12x0.1 x0.45
L= 0.54kg·m2/s
c)
L = I w1
0.54 = MR^2/2 w1
w1 = 135 rad/sec
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