The United States has begun air strikes on the militant Islamist group Islamic State (IS, formerly ISIS) in Iraq. President Barack Obama's decision to authorise the strikes followed reports that Iraqi and Kurdish forces had begun targeting IS sites on Thursday.

The beginning of US air strikes accompanies other humanitarian responses to the crisis. Earlier this week the US dropped water and food packages on Mount Sinjar, where about 40,000 people from the Yazidi minority are trapped by IS militants at the base of the mountain.

Obama has repeatedly stressed that any air strikes would be "limited" and that America will not be sending troops. "As commander in chief, I will not allow the United States to be dragged into another war in Iraq," he said. He's not aiming to wipe out all IS militants in Iraq, but instead to secure Kurdistan, a region of key military interest for the US.

Any military involvement in the Middle East understandably raises fears, both in the US and Britain. When Prime Minister David Cameron approached Parliament last year to sanction military strikes in Syria, the slap-down hit him hard. Similarly, Obama's U-turn and eventual decision not to respond militarily in Syria has marked him out as reticent to resort to military intervention, but this is not representative of his broader approach.

"He has mounted an unprecedented number of military strikes – in Pakistan, Yemen and Somalia," says Shashank Joshi, senior research fellow at the Royal United Services Institute. "He's not a president who's been afraid to conduct limited military strikes in specific cases, particularly in counter-terrorism.

"We remember him changing his mind on Syria because it's a prominent example and it did his credibility enormous damage."

Since the 2003 Iraq war, and the ultimate failure of the Libyan intervention in 2011 – which had been heralded as a prime example of successful interventionist policy – public scepticism about foreign intervention abounds.

Probably the biggest fear is mission creep – getting involved in a conflict that spirals out of control. But the present humanitarian situation also presses buttons. It is impossible for the international community to see endless pictures of crucifixions in Syria, children chopped in half in Iraq, tens of thousands trapped and dying of thirst – not to mention the hundreds of thousands who have had to leave their homes – without feeling that something must be done to stop the spread of IS. After all, food aid won't do anything to tackle the source of the problem.

In mid-June Obama held off implementing a military response in Iraq, so what is it about the present situation that warrants US involvement?

America's primary interest is in trying to protect Kurdistan, the semi-autonomous region in north-eastern Iraq, and the Americans sheltering there. When Baghdad was under threat from IS a few weeks ago, 275 American troops were sent in to help transfer American diplomatic and military personnel to Irbil, the Kurdish capital.

Kurdistan has long been one of the few safe, stable places in Iraq, and IS have shown relatively little interest in attacking the Kurds until now. By Thursday, four major towns on the path to Irbil had been captured, and it was thought that the militants were about 30 minutes away from the capital.

Traditionally, the Kurds have been pro-Western, and they supported foreign troops in the war against Saddam. More recently, the relationship between America and the Kurds has appeared stilted – possibly owing to the US' failure to support the Kurdish bid for independence from Iraq.

The US also has its joint operation centre based in Irbil, from which they are coordinating defences with the Peshmerga Kurdish forces that are fighting IS along a 600-mile frontier. It is unlikely that IS will be successful in capturing Irbil, but if they did, the ramifications would be enormous.

"Symbolically – I think by that time you've got to say the Kurdish project is finished," says Gerard Russell, a former British diplomat and author of Heirs to Forgotten Kingdoms: Journeys into the disappearing religions of the Middle East. "Practically it would be very serious too; they would have to take refuge in the mountains again, the road to Kirkuk would be open.

"In strategic terms, Sinjar is not particularly important, but the point is that unless [IS] are defeated, everyone in the Muslim world is going to look at them and think they are unstoppable. People will join them, as already is happening, and people will be scared of them and won't fight them, and people will do deals with them," Russell adds.

And what of the UK's involvement (or lack thereof?). The Archbishop of Canterbury, Justin Welby, has strongly condemned the Islamic State's brutal attacks, saying: "What we are seeing in Iraq violates brutally people's right to freedom of religion and belief.

"It is extremely important that aid efforts are supported and that those who have been displaced are able to find safety. I believe that, like France, the United Kingdom's doors should be open to refugees, as they have been throughout history."

But offering asylum isn't as straightforward as it sounds – and for once it's not a question of space. "It's part of the ISIS project to drive Christians out of the region," says Russell. "I fear that if that's the only thing we're going to do, we're frankly working towards the end of making the Middle East a far less diverse place.

"We should be intervening. We have to strengthen the Kurdish forces, who are the most likely to defeat ISIS in the Sinjar," Russell adds. "They were always our allies in the past... they are playing quite a tough political game with the Iraqi government, and that makes it awkward for us to support them at [this] time, but the big goal now must be to defeat terrorists who have been destroying Iraq's 2000-year-old tapestry of religions – not only that but pose a very serious threat to western countries."

So how effective will strikes be? "ISIS is a sophisticated force but it's vulnerable on open terrain – it can shelter in populated areas like Mosul and disguise its forces, but it can't do that on the roads on the way to Kurdistan and in open mountain areas," says Joshi.

A UK government spokesman has said that Britain won't be joining in any military response. This is meant to be a small, targeted campaign which shouldn't need British help. In fact, by not guaranteeing the use of force, Obama may have been hoping that Iraqi forces wouldn't need the US either, though clearly that hasn't worked. Let's hope this round of strikes will.