If there’s anger in JK Simmons, he puts it all on screen. He’s played a neo-Nazi psychopath and a foul-tempered newsman. His portrayal of a raging, violent conductor in the incendiary jazz thriller Whiplash has made him the frontrunner for the best supporting actor at the Oscars in February. He gives the performance of his career by bellowing at a roomful of whimpering milksops who just won’t keep the beat.

In person, Simmons is an avuncular gent, as drily good-natured as the cuddly dad he played in Juno. Whisked around the world on the award-season campaign trail, he’s treating it all – the deferential PRs, the earnest journos, the elaborate menu of this week’s five-star hotel – as an amusing oddity. After 20 years of supporting roles and being ninth on the call sheet, he’s happy to play the game and too experienced to take it seriously. At least this time he believes in what he’s selling.

“I’ve had some experiences in the last few years where my reticence to be involved in the publicity has not been helpful,” he says. “It’s so nice to be doing this as a part of a film that I can be unreservedly glowing about and not feel like I have to spin anything. I can be 100% honest and I don’t have to bullshit.”

Whiplash has plenty of momentum. It needs no more spin. Shot in just over two weeks, the second feature from 29-year-old writer-director Damien Chazelle stars Miles Teller as Andrew, a gifted jazz drummer seduced into a world of punishing exactitude by his brutal conservatoire teacher, Terrence Fletcher (Simmons). Fletcher – bald, muscular, black of heart and wardrobe – runs an ensemble like a military unit. He stops his band by clenching a fist. If his players mess up, he throws a chair at their heads. Then he takes them through the exercise again. And again. Through the night if need be. Fletcher doesn’t care about them, he cares about their talent. And he’ll do anything to force them to realise it. Make them play and play until they hit it.

There’s no “can do”, plenty of “screw you”. The band are all male, and Fletcher is liberal in his use of homophobic slurs. He will happily insult and upset to raise the standard. Dubbed Full Metal Juilliard by some critics, the film could come across as preposterously macho. But it’s Simmons’s commitment to Fletcher’s raging perfectionism that keeps you in the piece. You can’t laugh at Fletcher, no matter how silly his screaming about a dropped quaver seems. You’re too afraid to.

Facebook Twitter Pinterest Simmons with Miles Teller in Whiplash. Photograph: Moviestore/Rex

Whiplash argues that we’ve become soft. Encouragement is given too easily, punishment is seen as monstrous. The two most harmful words of the English language are “good job”, says Fletcher. Simmons doesn’t agree with the methods, but sometimes he can see Fletcher’s point.

“There’s a kind of numbness, a sameness, a lack of motivation in ‘good job’ culture,” he says. On this press tour, he’s been using the example of parents watching their kid on a playground slide. Gravity does all the work, then mum and dad go nuts. It really isn’t a cause for celebration.

“We’re raising a generation of kids who are being overly praised for incredibly minor accomplishments,” he says. “I think it’s counter-productive.”

Simmons, 59, was born Jonathan Kimble Simmons (he became JK when he started working in film, “well before Ms Rowling had her Potter books”). He grew up in Detroit, where his dad, Donald, was a college music teacher. There’s nothing of him in Fletcher, although Simmons’s sister, an English professor at the University of Washington, sends him clippings of Whiplash photos saying how much he looks like their father (“She hasn’t seen the movie yet”).

“Most of my friends – when I was five, six, seven years old – their dads were working in an auto plant in Detroit until 5.30 and then they were sat in rush hour,” he says. “They weren’t around as much. My dad finished at three o’clock, so he was just around more. He was ahead of his time in being a hands-on dad. This was the 50s and 60s. Dads would come home and sit and read the paper and the wife would fetch the slippers. He and my mother had a much more forward-thinking relationship”.

He moved to Ohio and spent his teenage years playing high-school football before his knees fell apart, forcing him to quit.

“I went from being a jock to a hippie,” he says. “It was a very clear-cut decision. I had to be one or the other. I had to forsake that other aspect of myself. Or thought that I had to, which is regrettable. Quickly, I was back in the pine trees with the hippies, listening to my Jimi Hendrix and my Janis Joplin and turning on, tuning in and dropping out.”

You could argue that, professionally, Simmons has been wandering between the football field and the pines ever since. After studying music composition at college and singing on Broadway, he moved into a TV career that saw him play stern, stylish hard arses. His recurring role as sceptical NYPD psychiatrist Dr Emil Skoda in Law & Order set up his stall as an authority figure. As Vernon Schillinger, the fascist rapist of the groundbreaking 90s HBO prison drama Oz, Simmons projected a terrifying persona despite his slight frame.

Facebook Twitter Pinterest With Ellen Page in Juno. Photograph: FoxSearch/Everett/Rex

His film characters tend to be more laidback. He played J Jonah Jameson for Sam Raimi’s Spider-Man films and was brutish, but only for comic effect. Jason Reitman, who Simmons credits for helping him make headway in movies, often casts him as a shambolic father figure, something that has stuck when he moved into the mainstream. Whether a garrulous IBS sufferer (in the Coen brothers remake of The Ladykillers) or a soft-hearted dean (in Hugh Grant romcom The Rewrite), Simmons tends to be the guy you’d be happy turning on, tuning in and dropping out with.

Perhaps this is why Fletcher is delivered with such conviction. He’s the actor’s first big-screen alpha male in a while: the uber-jock. The sports coach screaming on the sidelines as young, impressionable talent fails to meet up to his impossibly high standards.

Whiplash shares the structure of a classic sports drama. There’s the hot young talent, the grizzled old pro, the rise through the ranks and the inevitable price to pay. The last 20 minutes – the final game of the season – is a flat-out headrush, with Andrew hammering to make something of all of the blood, sweat and paradiddles.

Is Fletcher taking back some of the territory that, as a teenage hippy, Simmons left behind? Perhaps, he says. At the very least, the jock mindset still has its pull.

“I was talking to an old friend recently,” he says. “There had been a picture in the papers of me as Fletcher and he said: ‘Wow, man. You’re in really good shape! Flashing the guns!’ I was like: ‘There’s this inner ninth-grade jock who takes this great pride and satisfaction in that aspect of this character. The whole fucking macho thing that you develop as you hit puberty never goes away.’ His response was: ‘We all have that inner ninth-grade jock. Embrace it.’”

• Whiplash is released in the UK on 16 January