Posted by **Oisin** on Monday, August 9, 2010 at 10:03am.

(ii) For the wheel of diameter 10 cm, find its final speed after traversing a distance of 10 m down an incline of 25º. Assume it starts from rest.

I know i have to use the conversation of enrgy formula but how do i apply it to this instance?

- Physics -
**bobpursley**, Monday, August 9, 2010 at 10:26am
the change of height results in a change of energy:

changePE=changein KE

changePE= change in linear KE + change in rotational KE

that is the guiding energy relationship.

The key, is to relate angular rotation to linear speed, so you can combine the terms and solve. If the wheel does not slip, but rolls, you relate it this way:

condider a point on the wheel at the top, and the bottom, and the center of the wheel.

Assume the velocity down the hill at the center is v. THen the speed at the top must be wr+v (relative motion). The speed at the bottome is wr-v, but that has to be zero.

wr-v=0

or wr=v

Another way. Assume it went down the plane a length L in time t.

average velocity= L/t

maximum velocity=2L/t

rotations= L/2PIr

angular displaement= rotation*2PI=L/r

averge angular speed (rad/sec)=L/rt

final angular speed=2L/rt

so wfinal=2L/rt but t=2L/vfinal

final angular speed=2L/r*2L/vfinal=vfinal/r and again we get

wfinal*r=vfinal

You will have to make an assumption about the wheel for moment of inertia, that is, is it to be modeled as a disk,or a hoop. Most wheels a hoop works fine.

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