"We now have a museum that tells our 9/11 story"

The National September 11 Memorial Museum was dedicated Friday in New York City. The museum sits at the base of the fallen twin towers, next to an outdoor memorial.

President Obama, speaking at the dedication ceremony, recalled the heroism of Welles Crowther -- the 24-year-old "man with the red handkerchief" -- who helped many people trapped in the South Tower escape the crumbling building. Crowther had worked in finance on the South Tower's 104th floor.

Obama: 9/11 Memorial Museum a "profound and moving experience"

A red handkerchief like the one Crowther used that day is now on display at the museum. Obama said, "From this day forward, all those who come here will have a chance to know the sacrifice of a young man who, like so many, gave his life so others might live.

Obama said it was an honor to share the memories of the day and to "above all, to reaffirm the true spirit of 9/11 -- love, compassion, sacrifice, and to enshrine it forever in the heart of our nation."

"Like the great wall and bedrock that embrace us today, nothing can ever break us. Nothing can change who we are as Americans."

"All who come here will find it to be a profound and moving experience," he continued. "I want to express our deep gratitude to everybody who was involved in this great undertaking, for bringing us to this day, for giving us this sacred place of healing and of hope."

He added, "Those we lost live on in us. In the families who love them still, in the friends who remember them always, and in a nation that will honor them now and forever."

9/11 Museum remembers lost loved ones

The 9/11 memorial that opened two-and-a-half years ago lets visitors see from the outside where the twin towers once stood, CBS News' Jeff Glor reports. The museum takes them inside and underground, and there is little held back. Steel from the south tower that split open is on display, along with a mangled fire truck, a bloody shoe and, echoing in the halls, voices of those who died.

Lauren Grandcolas left her husband a message from Flight 93. She can be heard saying via a recording, "Honey, I just love you. Please tell my family I love them, too. Bye honey."

Alice Greenwald, the museum's director, said, "At the heart of this museum is a fundamental conviction - that bearing witness to the unimaginable is the only way to imagine a way beyond it."

The nearly 13 years leading up to this day were full of delays and some disagreements: One, over how much to include about the hijackers; another, over whether to house the remains of the unidentified victims on site. They will be, but not on display for the public.

Anthony Gardner lost his brother Harvey. He fought hard to preserve box beam columns that mark exactly where the towers stood. Gardner said, "We now have a museum that tells our 9/11 story. It's just going to have a tremendous impact on people, I think, as they come through these sacred spaces."

There's also the cavernous Foundation Hall - sided by a slurry wall that never gave way - and the "Last Column," removed from the site in May 2002, is now covered with tributes from first responders and family members.

If there's too much to absorb at once, part of that was by design. Greenwald said, "If people aren't sad here, we've done something wrong, but that isn't the end of the story. This is a museum about hope."

Victims' families will be able to visit the museum beginning Thursday. It doesn't officially open to the public until next Wednesday. There is a $24 fee to enter. The museum says it should be free, but to do that, they need federal funding.