New Twiddle

components.my-component.js

import Ember from 'ember';

export default Ember.Component.extend({
  classNames: ['classname-1', 'classname-2'],
  classNameBindings: ['class4:classname-4'],
  
  actions: {
    
    // Add class3 using jquery
    addClass3: function() {
      this.$().addClass('classname-3');
      this.setClasses();
    },
    
    // Toggle the class4 property, which makes the binding update
    toggleClass4: function() {
      this.toggleProperty('class4');
      this.setClasses();
    }
  },
  
  setClasses: function() {
    Ember.run.scheduleOnce('afterRender', this, function() {
    	this.set('classes', this.$().attr('class'));
    });
  }.on('didInsertElement')
});

controllers.application.js

import Ember from 'ember';

export default Ember.Controller.extend({
  appName: 'Ember Twiddle',
  
});

templates.application.hbs

<h1>Welcome to {{appName}}</h1>
<br>
<br>
{{outlet}}
{{my-component}}
<br>
<br>

templates.components.my-component.hbs

<p>Classes are: {{classes}}</p>

<button {{action "addClass3"}}>Add class3 with jQuery</button>
<button {{action "toggleClass4"}}>Toggle class4 through binding</button>

twiddle.json

{
  "version": "0.10.6",
  "EmberENV": {
    "FEATURES": {}
  },
  "options": {
    "use_pods": false,
    "enable-testing": false
  },
  "dependencies": {
    "jquery": "https://cdnjs.cloudflare.com/ajax/libs/jquery/1.11.3/jquery.js",
    "ember": "2.8.2",
    "ember-data": "2.9.0",
    "ember-template-compiler": "2.8.2",
    "ember-testing": "2.8.2"
  },
  "addons": {}
}