I'll 2nd Phil's comments. 50mm is the 'normal' angle of view lens on a 35mm or full frame digital camera.
Approximately the length of the diagonal across the frame.. if you do the Pythagorean squaw on the hippopotamus is equal to the saws on the other two hides, for the 24x36mm frame size of a 35mm neg, it actually works out at 43&1/4mm.. hence the anomaly of the Helios 44, that was a 'standard angle' lens for a 35mm camera at 58mm focal length ?!?!?!
On a crop sensor DSLR the 'standard angle of view' lens length is closer to 35mm ... do the hipopotomus hides again, though, for Nikon APS-C sensor at 16x24mm and it should be 28.8mm.
A lot of 'academic' exercises offered in the books back in the film-only era, were based around the 50mm lens, as that was what came as standard with most entry level 35mm SLR's, and like modern 'standard' 18-55 ish kit zooms these days, they were often pretty cracking bits of kit for the money... effectively 'free'! so the accademic excersises were based around them to teach photography and how to get the most from the equipment you most likely already had, and gaining know-how rather than gadgets.
Carried over into the Digital era, a lot of the legacy of the 50 on film has come through, omitting the 'crop factor', that 'really' a lot of the academic exercises suggested should be translated to crop-sensor digital at around 30mm rather than 50mm; whilst in the film only era 50's were the 'standard' lens you got with the camera 'for free', and were often the first one to be ditched in favor of telephoto's or wide angles or zooms. They were, then, frequently to be found very cheaply in the 2nd hand shops, or simply given away! I had about three, now quite sought after, OM-fit Zuico 50's 'back in the day' including the rare f1.4 version! that came as standard with my OM4, that I DID just give away, as I NEVER used them. by the time digital came along, zooms were an accepted standard, and there weren't many 'prime' lenses on offer for them; But there were plenty of old manual focus and a couple of potentially compatible with AF Digital, auto-focus 50's knocking about from the film era, often at incredibly depressed prices, giving rise to the vogue for folk to ignore the crop factor on digital anomoly and step into the arena of prime lens photography with them... which is what prompted Nikon to actually offer the AF-S 35 f1.8, that gives 'close' to that standard angle on a crop sensor DSLR, and will Auto-focus on entry level focus 'lens motor only' cameras.
Which is all background to the answer; which is basically as has been said; NO you don't 'need' a 50. Suggestion, IF you want to delve into this world of prime lens photography, where much faster apertures to allow much shallower Depth of Focus effects, and or low light situations to be exploited; and you have to apply that much more thought and attention to framing and composition, without a zoom suggesting you can frame from wherever you happen to be standing, and engage in some of the more traditional academic exercises and learn the 'diligence and discipline' of working with more limited equipment they were trying to teach, then, yeah... a 50 might be 'useful', but on a crop sensor camera, a 30 or 35 (probably the Nikon AF-S f1.8 35) may be the more appropriate.
Having said I gave away my OM 50's back in the day from lack of use; that was because whilst I was doing my C&G photography, I got into 'primes' in M42 screw fit on a rather nice Ricoch 'copy' sigma MK1 with a Ziess 50, and a number of 'charity shop' special roll film cameras we were encouraged to go find and mess with! However, my daughter doing O & A Level photography, 'stole' my DSLR, and after some rather heart atack enducing experiments with water filled baloons and then waterfalls in the bath!!!!! I bought her her own DSLR body, and as she was starting to run into the buffers of what she was trying to do with my 18-55, I paired it with a Nikon AF-S 35, for her to get started with, and do her accademic exercises; later I got her the Nikon AF-S 50, to go with it, when she was starting to do portraiture in the studio, again for accademic exercises.So, either or both 50 or 35 primes can be very very useful, IF that's what you are trying to do, or the way you are thinking of heading; BUT, neither are lenses I would put on as a general walkabout instead of the 18-55!