In the figure here, a cylinder having a mass of 1.9 kg can rotate about its cent

Question

In the figure here, a cylinder having a mass of 1.9 kg can rotate about its central axis through point O. Forces are applied as shown: F_1 = 3.7 N, F_2 = 2.2 N, F_3 = 4.3 N, and F_4 = 2.0 N. Also, r = 1.9 cm and R = 12 cm. Taking the clockwise direction to be negative, find the angular acceleration of the cylinder. (During the rotation, the forces maintain their same angles relative to the cylinder.) The figure shows a uniform disk that can rotate around its center like a merry-go-round. The disk has a radius of 2.0 cm and a mass of 23 grams and is initially at rest. Starting at time t = 0, two forces are to be applied tangentially to the rim as indicated, so that at time t = 1.2 s the disk has an angular velocity of 250 rad/s counterclockwise. Force has a magnitude of 0.102 N. What is magnitude F_2?

Explanation / Answer

052)
Torque due to F1,
T1 = F1*R = 3.7 N*0.12 m = 0.444 Nm

Torque due to F2,
T2 = - F2*R = -2.2 N*0.12 m = -0.264 Nm

Torque due to F3,
T3 = -F3*r = -4.3 N*0.019 m = -0.0817 Nm

Torque due to F4,
T4 = F4*0 = 0 Nm

Tnet = 0.444 -0.264 -0.0817 = 0.0983 Nm
I = 0.5*m*R^2
= 0.5*1.9*(0.12)^2
= 0.01368 Kgm^2

use:
Tnet = I*alpha
0.0983 Nm = 0.01368 Kgm^2 * alpha
alpha = 7.19 rad/s^2
Answer: 7.19 rad/s^2

I am llowed to answer only 1 question at a time

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