A police officer slams an unarmed 15-year-old girl in a bikini to the ground, pulls his gun and kneels on her as teens on either side of him shout and, of course, record the encounter. Within hours, millions watch the video: Some see a defenseless black teen being manhandled by an out-of-control white cop; others see a lone, scared officer in the crowded, chaotic aftermath of a fight he doesn’t yet understand. Cellphone video has become as much a part of policing as tickets and handcuffs. Video images of police shootings have sparked national turmoil. But Friday’s ugly, cacophonous...