Absolute Value Signs, Inequalities and Mechanics (1 Viewer)

[frog1944]

Hi,

Context: When looking at the 2007 HSC Q 3 d) ii) where they asked for what values of w is N >), the MANSW solutions obtain that w^2 < g/rtan(Theta), and then state |w| < (g/rtan(theta))^0.5 . However, for the 2016 HSC Q 13 c) ii) they asked for what range of values of w is T_2 > T_1, their solutions state |w| > (200/3)^0.5) and then say w > 0, thus w > (200/3)^0.5 (though I couldn't find in the question that w>0)

Question: Is there a discrepancy between the different tests and their solutions? Or could someone please explain why for the 2016 w>0?

Thanks

 

[raz999]

The truth is in circular motion, the angular 'velocity' w is really angular speed, i.e. w is ALWAYS defined to be > 0. Hence |w| makes no difference.

 

[frog1944]

Ok, so in the HSC I should always just take the positive root of w, as w is always > 0?

 

[pikachu975]

Ok, so in the HSC I should always just take the positive root of w, as w is always > 0?

Yes and write w>0 in brackets

 

[frog1944]

Great! Thanks guys, will do