The cylinder shown in the figure, with mass M and radius R,...

The cylinder shown in the figure, with mass M and radius R, has a radially dependent density. The cylinder starts from rest and rolls without slipping down an inclined plane of height H. At the bottom of the plane its translational speed is sqrt{8gH/7}. What is the rotational inertia of the cylinder?

Transcript

00:01 The cylinder is the cylinder shown in the figure with mass m and radius r has a radiary dependent density.

00:06 The cylinder starts from rest and rolls without slipping down the inclined plane of height edge.

00:12 At the bottom of the plane, its transitional speed is what is the rotational inertia of cylinder.

00:18 So here it is we can see that.

00:27 We can see that here.

00:29 This is the diagram with the radius of height h.

00:51 This is m.

00:58 Now we can say that here by conservation of energy energy at a and b so ea equal to e b now we can write here m g h n plus k e e equal to m g hb plus k e p b plus k e r b so we can write here now h a equal to h v a equal to 0 w equal to 0 and r h b equal to 0 and b b equal to v b equal to w b equal to w equal to b divided by r so we can write here put all value in equation one so we can write here m g h plus one divided by two m zero squared plus one divided by two i zero square equal to m g multiply zero plus one divided by two m b squared plus one divided by two m b squared to i w square so we can write here m g h equal to 1 divided by 2 m b squared plus 1 divided by 2 i b divided by r square so m g h equal to 1 divided by 2 m under root 8 g h divided by 7 square plus 1 divided by 2 i divided by r squared under root 8 dh divided by seven squared now we can write here 7 divided by 4m equal to m plus i divided by r squared so we can write here 7 divided by 4 m minus m equal to i 7 divided by r squared so 7m minus m equal to i divided by r squared so 7 m minus m divided by 4 equal to i divided by r squared so 3m divided by 4 equal to i divided by r squared so we can write here i equal to 3m r squared divided by 4 i'm said now we can write here for no slipping v equal to r w or equal to v divided by r so we can write here by conservation of at position a and b.

05:19 So we can write here of a and b.

05:45 So we can write here ea equal to e b...

Question

Please give Ace some feedback