Rotational Motion

I found the moment of inertia of R, but then i don't know how to solve this further, It's a great help if someone can explain me how to solve this

The diagram is a bit misleading as the step height is 1/2 the radius of the disk.

You're looking at a rotating disk having enough energy to rotate about the point of contact with the step and move up. I'd imagine the key is to consider the moment (energy) about the point of contact with the step (hence the calculation in part a) and use conservation of energy to get it to move up.

This is slightly beyond my knowledge in rotational problems, but I think you might have to use conservation of angular momentum.

Not sure I can use conservation of angular momentum because there is a component of the weight of R, perpendicular to the line AC

I feel like the angular speed omega must be a function of time rather than a constant as it reduces when it goes up..

$\omega$ is the angular speed immediately after impact. It doesn't refer to the speed throughout the subsequent motion. Conservation of angular momentum is the way to go.

I feel like the angular speed omega must be a function of time rather than a constant as it reduces when it goes up..

After the impact, think about energy. You're told omega is after the impact.

Okay, Thankyou...

$\omega$ is the angular speed immediately after impact. It doesn't refer to the speed throughout the subsequent motion. Conservation of angular momentum is the way to go in dealing with the impact itself.

Edited: for clarity.

You seem to have calculated the linear momentum before the impact, not the angular... (Edit, or you've ignored the rotational angular momentum of the wheel before the impact, or something...)

I know what you suggest gives the given answer (and I'm sure is the expected approach), but are you sure angular momentum would really be conserved? (I don't think it would be unless the step is perfectly smooth).

My reasoning is that since we are considering motion about the point A, then any impulse due to the impact would have zero moment, and so angular momentum is conserved.

Need a help please