A disk, initially rotating at 170 rad/s, is slowed down with a constant angular

Question

A disk, initially rotating at 170 rad/s, is slowed down with a constant angular acceleration of magnitude 9.0 rad/s2. A disk, initially rotating at 170 rad/s, is slowed down with a constant angular acceleration of magnitude 9.0 rad/s2. In the figure below, two blocks, of mass m1 = 270 g and m2 = 780 g, are connected by a massless cord that is wrapped around a uniform disk of mass M = 500 g and radius R = 12.0 cm. The disk can rotate without friction about a fixed horizontal axis through its center; the cord cannot slip on the disk. The system is released from rest. (a) Find the magnitude of the acceleration of the blocks. 10.992-Ox m/s2 (b) Find the tension T1 in the cord at the left. (c) Find the tension T2 in the cord at the right.

Explanation / Answer

given

m1 =270 g

m2 = 780 g

M = 500g

R = 12cm

(a)

for block 1
T1 - m1*g = m1*a ..........eq1

for block 2
m2*g - T2 = m2*a .........eq2

for pully

R*T2 - R*T1 = (1/2 M R^2 )*alpha

R*T2 - R*T1 = (1/2 M R^2 )*a/R

T2 - T1 = 1/2 *M *a  .............eq3

add equations

m2*g - m1*g = m1*a + m2*a + 1/2 *M *a

a = m2*g - m1*g /(m1+m2+M)

a = 0.78*9.8 - 0.27*9.8 / (0.78 + 0.27 + 0.5)

a = 3.22 m/s2

(b)

from eq1

T1 = m1*(g+a)

T = 0.27 *(9.8 + 3.22)

T = 3.51 N

(c)

from eq2

T2 = m2*(g-a)

T2 = 0.78*(9.8 - 3.22)

T2 = 5.13 N

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