I guess the common term for this in the valley would be to pivot.
If we raised money from angel investors, and it turned out the startup isn't going to succeed, could we pivot the company to a completely different idea and use the remaining funds?
i.e. The corporate entity would still remain the same and the investors would still have the same ownership in the new idea of the startup.
Is this common or something that investors frown upon?
Starting a new company and pivoting aren't the same thing. Pivots usually leave you still working on the same general product. Forming a new legal entity and funneling cash into it from the first company could get you into legal trouble.
Having said that, your investors know that nearly every company will require a pivot of some sort, and in some cases, you may discover that your original idea just isn't even in the right ballpark.
When you discover the need to pivot (or start over with a fresh idea) the ethical thing to do is to meet with your investors and figure out as a group what the next step should be. Depending on the contracts and agreements you've made, there's a good bet you'll even be required to do this.
In talking with them, they may feel like they'd rather recover unspent cash and call it quits (perhaps they invested in the original idea, and a change in product just isn't something they're interested in). Or perhaps they've got a different pivot that they want to try first before switching ideas/companies first. Of course, it's also a possibility that they've invested in the team itself, agree with your assessment that it's time for a different product altogether, and be totally on board with changing to something different.
The options you have available to you will depend on what you've signed in the past, who has what percent of the equity, and what you can agree to.
In short, yes, you could possibly pivot to a completely different idea, but you need to talk it over with your investors.
If you feel the need to switch legal entities, talk with you lawyer and accountant to make sure you transfer the funds in a way that doesn't get you in legal trouble or force you to pay a lot in taxes.