Edit in JSFiddle

var myApp = angular.module('myApp', []);
myApp.controller('myController', ['$scope', '$sce', function($scope, $sce) {
    //$scope.video = "http://www.youtube.com/embed/6Ejga4kJUts";
    $scope.embed = "http://www.youtube.com/embed/";
    $scope.video = "6Ejga4kJUts";
    $scope.src = $sce.trustAsResourceUrl($scope.embed + $scope.video);
    
    $scope.change = function() {        
        $scope.src = $sce.trustAsResourceUrl($scope.embed + $scope.video);
    }
}]);

<div ng-app="myApp" ng-controller="myController">
    ID de Video deYoutube: <input type="text" ng-change="change()" ng-model="video" style="width: 200px;" /><br/>
   <iframe width="420" height="315" src="{{src}}" frameborder="0" allowfullscreen></iframe>
</div>