M2 help

http://www.ocr.org.uk/Images/144604-question-paper-unit-4729-01-mechanics-2.pdf

Q8ii.

Can someone explain what the question is asking. Does the friction have to be greater than the reaction for it not to slip? idk

At the max possible speed, friction will act in the opposite direction to previously (so towards V) since the particle will want to spin out of the circle and up the slope.

Someone can probably explain that in more mathematically correct terms but that's kind of the idea behind it.

Sorry I don't get why friction is down, even though you have sort of explained :/

Someone can probably explain that in more mathematically correct terms but that's kind of the idea behind it.

Reaction force is perpendicular to the surface, friction is perpendicular to reaction. So friction acts parallel to the surface. In the first bit of the question, the friction acts upwards because the natural tendency of the particle is to slip down the slope.

In the last part of the question, you want to maximise the angular speed with the constraint that the particle doesn't slip. That is, if you increase the speed beyond this maximum angular speed, the particle will spiral or 'slip' upwards. Friction opposes motion and acts down the slope instead.

Furthermore, you'll want to use the limiting value of friction in order to maximise centripetal acceleration and hence maximise angular velocity.

tl;dr:

Minimum angular speed occurs when the particle is going to slip downwards, because if it goes any slower it falls down the slope so friction acts upwards.

Maximum angular speed occurs when the particle is going to slip upwards, because if it goes any faster it flies up the slope, so friction acts downwards.

Friction opposes motion.

Brilliant! Got it