What Is the Initial Acceleration of End B When the String Is Cut?

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SUMMARY

The initial acceleration of end B of a rod, when the supporting string is cut, is calculated using torque and Newton's laws. The rod, measuring 57.0 cm in length and weighing 1.90 kg, experiences an angular acceleration of 207.8 rad/s². This value is derived from the torque equation, where torque equals the moment of inertia multiplied by angular acceleration. The final linear acceleration at end B is determined to be 118.4 m/s², confirming the calculations based on the principles of rotational dynamics.

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A rod of length 57.0 cm and mass 1.90 kg is suspended by two strings which are 41.0 cm long, one at each end of the rod. The string on side B is cut. Find the magnitude of the initial acceleration of end B.

I tried using torque= I* alpha
torque= L x f= (.57)(18.62)=10.6
I got from Newton's 2nd law, (9.8)(1.90)
so, 10.6 = I* alpha
I= (1/12)(mL^2)= (1/12)(1.90 * (.57)^2= .051
so, 10.6 = .051 alpha
alpha = 207.8 rad/s^2
alpha= a/L
207.8 = a / .57
a= 118.4 m/s ^2

This isn't right... can someone please help me?
 
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First, the place that it is rotating around is at one end of the rod.
How far from this is the rod's center-of-mass?

Second,
Newton's 2nd law is "Sum of Forces = ma"
Maybe you mean Newton's 4th Law "Force by gravity = m g = m GM/r^2"
 

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