Rotational Motion Problem - 11

1. Dec 16, 2013

coldblood

Hi friends,

The problem is as:

https://fbcdn-sphotos-a-a.akamaihd.net/hphotos-ak-prn2/q71/s720x720/1503374_1461728057387633_909744247_n.jpg

Attempt -

https://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-prn2/1506899_1461728417387597_658199054_n.jpg

2. Dec 16, 2013

haruspex

a = Rα is for rolling contact.

3. Dec 17, 2013

coldblood

Yes But centre of mass of the sphere woild be going with Translational acceleration,
Whose value would come from the bottom point in contact using, a = rα
Isn't it?

4. Dec 17, 2013

haruspex

No, as I said, that's only for rolling contact. When the spinning cylinder is placed on the plank it will skid at first. Suppose frictional force is F. What linear acceleration will that produce? What torque? What angular acceleration?

5. Dec 17, 2013

coldblood

https://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-ash4/1506955_1462163254010780_1540770628_n.jpg

6. Dec 17, 2013

haruspex

That's all correct, but what you are asked for is a. Your remaining step is to figure out what f is in terms of m, g and mu.

7. Dec 17, 2013

coldblood

Well, here a is f/m and f will be, μmg/m = µg(i)
and acceleration of plank would be µg(-i)

so acceleration of sphere w.r.t. plank would be 2µg.

Is that correct?

8. Dec 18, 2013

haruspex

That's it. You didn't need to worry about the rotations at all!