00:01
We know that the cylinder has both translational and rotational motion.
00:04
We can also apply newton's second law to the cylinder because, of course, it does, we have forces.
00:13
And we can say that first, the sum of the forces, this would be for part a.
00:19
Some of the forces in the y direction.
00:21
This will equal the mass times the acceleration in the y direction.
00:25
This will become the tension minus mg, the weight, equaling the mass.
00:31
Multiplied by negative a, the negative linear acceleration, or we can say that then the tension force is going to be equalling the mass multiplied by g minus a.
00:41
Now, we know that the net torque or the sum of the torques is going to be equaling the moment of inertia multiplied by the angular acceleration.
00:49
We can then say that negative t r would be equalling i, the moment of inertia, multiplied by negative a, the linear acceleration divided by r, substituting in for the angular acceleration.
01:04
And so for a uniform solid cylinder, we can say that the moment of inertia will be equaling one half mr squared.
01:13
And so we can then say that tr equals mr squared over 2 multiplied by a over r, or essentially the linear acceleration equaling two times the tension force divided by the mass itself.
01:31
Now we can plug this into our previous equation here and we can say that then the tension force is going to be equaling mg minus 2t.
01:45
Or we can say that then the tension force will be equalling mg divided by three.
01:51
This would be our final answer for part a.
01:55
For part b, we know that the acceleration is equaling two times the tension force over m...