Two disks of radii R_o = 200 mm and R_i = 100 mm are glued together. The total m

Question

Two disks of radii R_o = 200 mm and R_i = 100 mm are glued together. The total mass of the disks is m_D = 20 kg and the combined moment of inertia about the z-axis passing through their common center O is I = 1.6 kg m^2. A string attached to and wrapped around disk B supports a mass in = 2 kg. The string wrapped around disk A is pulled with a force F = 20 N as shown in Fig. Assume there is no slip between the strings and the disks. Find the angular acceleration of the disks, the tension in the string supporting mass m, and the acceleration of mass m.

Explanation / Answer

Here,

Ro = 200 mm

Ri = 100 mm

mD = 20 Kg

I = 1.6 Kg.m^2

1) let the angular acceleration of the disk is a

acceleration of the mass m is at

let the tension in the cable is T

Using second law of motion

F* Ro - T * Ri = I * a

20 * 0.2 - T * 0.1 = 1.6 * a ------(1)

for the block

2 * 9.8 - T = -2 * at

as at = a * 0.10

2 * 9.8 - T = -2 * a * 0.10 ----(2)

solving 1 and 2

a = 1.29 rad/s^2

T = 19.85 N

1)

the angular acceleration of the disk is 1.29 rad/s^2

2)

the tension in the string is 19.85 N

3)

acceleration of mass m = a * 0.10

acceleration of mass m = 1.29 * 0.10 m/s^2

acceleration of mass m = 0.129 m/s^2

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