Barack Obama has rhythm. And timing. And on a sweltering Brisbane day, enough cool, maybe, to change the climate.

He also has the authority of the President of the United States to pull a vision from the heavens, and the gift granted to perhaps one leader in a generation to make a whole room believe in it.

All the things, the cruel might reflect, that appear to elude Australia's current Prime Minister who, given the opportunity to address the world's leaders, had them politely coughing into their hands when he yacked on about a $7 doctors' co-payment and celebrated the end of a carbon tax.

So there, for purposes of comparison, was Obama a bit later in a Queensland University auditorium configured like a basketball stadium, the crowd pumped, a White House soundtrack turned up LOUD. Here were the Staple Singers, gospel-promising I'll Take You There; here was Springsteen, American rock 'n' roll declaring We Take Care of Our Own, Jackie Wilson blasting out Your Love Keeps Lifting Me Higher and, yes, Stevie Wonder, making the soul promise: Signed Sealed, Delivered.

And here came the President, that slim-line swing of his; a mere lifting of the hand drawing the 900 students ranked in the bleachers to their feet.

"I love being in Australia, I really do," he cracked. "The only problem is I've got to sit in conference rooms and attend meetings instead of going to the beach."

You'd think Obama had it signed, sealed and delivered right there, half the crowd fairly swooning at his little half smile, but he was just getting into stride.

There was that vision he wanted to offer, but being a man of timing, he was going to build up to it. He mentioned his 31 million Twitter followers – "just bragging a little bit" – how he'd been travelling all week and thus didn't know what time it was and how (chuckle) when he arrived he "needed a XXXX" beer.

He was into the rhythm now, swinging into a dissertation on the paths the world might take and how he wanted peace over disorder, liberty over oppression, and how his administration would focus its attention on the Asia-Pacific, where generations of Americans had died in the cause of liberty.

And then, click, he changed gear. The moment he uttered the words "climate change" all those students began cheering.  No nation was immune from the danger, Australia faced more droughts and more wildfires, and the President wanted to be able to come back to the Great Barrier Reef and bring his daughters, and he wanted them to be able to bring their children.

Keep raising your voices, he told the students. It was the nature of the world that "those of us getting grey hair are a little entrenched in our views".

He had them roaring again when he promised to "stand up for our gay and lesbian brothers and sisters".

And then he plunged into the crowd, hands reaching out for him, and the soundtrack, LOUD, was all folksy plucking of banjo strings and soaring guitars, a rhythmic, cool Keith Urban thing called Somebody Like You, and for a moment there, it might have been composed for Obama himself.