based on the World Pool-Billiard Association (WPA) World Standardized Rules (the “official rules of pool”)

Is it a foul to hit “into” a cue ball frozen to an object ball?

No. Under the WPA “official rules of pool,” when the cue ball is frozen to the object ball, you are allowed to hit into the cue ball toward the frozen ball with a normal stroke since the shot does not result in a push or a double hit:

In fact there are aiming systems devised just for this type of shot. High-speed video footage clearly shows that hitting into a CB frozen to an OB, with a normal stroke, results in a non-pushing, clean hit, just like any other legal shot. Examples can be found in NV B.48, HSV A.96, and HSV A.97. These shots might “feel” like push shots, but they are not. Examples of true push shots can be found on the push shot foul resource page.

Now, if there is a miscue during a frozen CB shot, it could be ruled a foul if there are obviously multiple hits or if the miscue is intentional. HSV 7.5 is an example that is tough to call, even with high-speed video.

For many example calls along with explanations, see the following videos:

Here’s an interesting example of a frozen-CB shot. The CB is frozen to the 8. Both the CB and 8 are driven toward the 9 with a slight cut angle. The CB hits the 8 a 2nd time after the 8 deflects off the 9. There is no double hit or push with this shot.

Why does the OB separate from the CB slightly with a straight center-ball hit into a frozen CB?

The CB and OB remain in contact as the tip pushes and accelerates them both forward together. After the CB and OB separate from the tip (together as one, still in contact with each other), the OB then separates from the CB slightly. Here’s an old low-quality video that sorta shows the effect:

As the tip pushes both balls forward together, the OB starts to roll very slightly (since there is very little friction between the CB and OB as compared to between the OB and the cloth). During most of the time the tip is in contact with the CB, the CB does not rotate (because there is a lot of friction between the chalked tip and the CB). Therefore, when the CB separates from the tip, both balls have the same forward speed, but the OB has a small amount of topspin that helps it separate from the CB very slightly.

There are other physics effects going on (with elastic waves and vibrations in the cue and balls during contact) that can also explain why the OB might leave the CB at slightly more speed when the tip separates from the CB, but these effects are small and unimportant in the grand scheme of things.

Should the cue be required to be at 45 degrees or more to prevent possible arguments about possible double hits or pushes with a frozen CB?

No! See:

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