10/26/2017 Suggested 10.2 A disk of radius 0.4 m and moment of inertia 1.1 kg·m2

Question

10/26/2017 Suggested 10.2 A disk of radius 0.4 m and moment of inertia 1.1 kg·m2 is initially at rest. At t = 0, two force F, = 3 N and F2 = 12 N are applied to the disk as shown in the figure, and the disk begins to rotate about its center. The angle = 30°·The forces maintain the indicated angles during the rotation. a. What is the net torque acting on the disk? Indicate the direction with the 9 9 sign of your answer. 4.2 N-m b. What is the angular acceleration of the disk? Indicate the direction with the sign of your answer. 3.82 rad/s2 What is the angular speed of the disk after it turns through one revolution? c. 9 0 2 6.93 rad/s

Explanation / Answer

a) Net torque acting is Tnet = Torque due to F1 + Torque due to F2

Tnet = (-0.4*3*sin(30))+(0.4*12*sin(90))

Tnet = 4.2 N-m

b) angular accelaration is alpha
and given I = 1.1 kg-m^2

Torque Tnet = I*alpha

alpha = Tnet/I = 4.2/1.1 = 3.82rad/s^2

c) initial angular velocity is wo = 0 rad/s

final angular speed is w

angular dispalcement is 2*3.142 rad

then using

w^2 - wi^2 = 2*alpha*theta

w^2 - 0^2 = 2*3.82*2*3.142

w = 6.93 rad/s

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