00:01
Hello, here we have to solve the following problem.
00:03
We have to determine in which order the objects arrive to the bottom of the incline.
00:08
Here we have sphere, solid cylinder and hollow cylinder.
00:25
Let's call them, let's call the moment of inertia i1, 2 over 5 mr squared i2, which is mr squared over 2 and i3, mr squared.
00:41
And let's now make the sketch.
00:44
Here let's show the gravity acting downwards and in addition there is a normal reaction and the friction force which prevents it from slipping.
00:55
Here acceleration is downwards and ma equals to mg sin alpha, where alpha is a slope minus friction force.
01:07
This static friction force is coefficient of static friction mg cosine alpha.
01:13
Then acceleration is g times sin alpha minus coefficient of static friction cosine alpha.
01:21
You need to find this acceleration, we need to find this coefficient.
01:27
So now let's look at this point of the contact point a.
01:32
At point a, static friction force equals to moment of inertia times angular acceleration over r.
01:50
All right, and now let's see how we could have simplified these equations...