A cord is wrapped around each of the two 20-kg disks. They are released from res

Question

A cord is wrapped around each of the two 20-kg disks. They are released from rest. Suppose that r = 76 mm. Neglect the mass of the cord. (Figure 1) Determine the angular acceleration of disk A. measured clockwise. Express your answer using three significant figures. Enter positive value if the angular acceleration is clockwise and negative value if the angular acceleration is counterclockwise. Determine the angular acceleration of disk B, measured clockwise. Express your answer using three significant figures. Enter positive value if the angular acceleration is clockwise and negative value if the angular acceleration is counterclockwise. Determine the tension in the cord C. Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

Here ,

m = 20 Kg

r = 76 mm = 0.076 m

part A) let the tension in the string is T

angular acceleration of A is aA

angular acceleration of B is aB

as the torque on both is equal , angular acceleration of pulley will be same
aA = aB

for the disk B

20 * 9.8 - T = 20 * aA * 0.076 -----(1)

for A

T * r = 0.5 * m * r^2 * aB

T = 0.5 * 20 * 0.076 * aA -----(2)

solving for 1

-0.5 * 20 * 0.076 * aA + 20 * 9.8 = 20 * aA * 0.076

solving for aA

aA = 86 rad/s^2

the angular acceleration of pulley A is 86 rad/s^2

part B)

the angular acceleration of pulley B is 86 rad/s^2

c)

for the tension

T = 0.5 * 20 * 0.076 * 86

T = 65.4 N

the tension in the string is 65.4 N

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