How to judge direction of motion?

Question

I have this scenario

suppose a cylinder is made by joining two symmetrical cones and is given a gentle push on two rails A and B . What will be the motion of cone . Will it turn right or left

I think that since friction is acting backwards on both the cones but friction on side AB is at an angle while friction on CD is perpendicular to centre o, the torque due to $f_{CD}$> $f_{AB}$  so system tries to rotate in a clockwise sense resulting it in turning right but the answer says its left .
I don't find the mistake in my answer.

Anusha · Accepted Answer

This can be judged by observing the motion in future

In due moment of time we see the distance between centre and left rail decreases but in order to ensure that rolling occurs the cone will have to bent as seen in last diagram which indicated it has turned left

Danny LeBeau · Answer

I will give you 2 hints.

Assume that the body never turns .
Then at some distance x calculate linear velocity both cones about the centre.

Hints: 1. in pure rolling linear  velocit is given by rw.

W is same for both bodies as it is a rigid body.

How to judge direction of motion?

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