00:02
So for this problem, the first thing to note is that the force acting on the collar due to the spring is equal to the force constant of the spring k into r minus the position of a, r a.
00:19
Now for part a, we have that the theta component of the force is equal to zero.
00:29
And at a, the radial component of the force, so this force always only has a radial component.
00:37
But at a this radial component is minus f due to the spring and this force is equal to zero as the spring as the collars have constant so if the resultant force on the spring is zero we have that the acceleration in either component is both zero so the radial component of the acceleration of the color at a is zero and the theta component of the acceleration of the collar is also zero.
01:18
So there is no acceleration of the collar at this point.
01:24
So that's our first answer, our answer for part a.
01:28
Part b, we'll use the fact that the sum of the radial component of all the forces must equal to m .a .r.
01:40
Where a is a r is the radial component of the acceleration.
01:45
So what this means is that the force due to the spring is equal to m times r double dot so this is a minus r theta dot squared so m into d2 r d t squared minus r d theta d squared and we note that the acceleration of the collar relative to the rod is simply d to r d t square, the second derivative of the position, or the first derivative of the acceleration...