Dips

[hellboy3]

How do you prevent yourself from using the momentum in your legs to help you during the dips or pull-ups?

[Mustrainhard]

Use the abs and hip flexors to stabilize oneself, and also performing them slowly to reduce momentum buildup in the first place.

[Fitness-Chic]

Yeah, If you are just whippin them out like there is no tomorrow then of course you are going to use some momentum there. Slow and controlled is the way to go.

It's not a race to see how many can be done in one shot...lol ( Sorry I'm being a smart ass here ).
You should be using controlled movments and focusing on the main muscle being trained.

[Twerp]

For Dips, if you're doing the full range of motion (shoulders at or below elbows), it's pretty much impossible to use momentum without hurting yourself. Slow down and do them right.

As for pull-ups, the starting and finishing point for a pull-up/chin-up is a dead hang at the bottom i.e. no bend in the elbows and no momentum. The mid point should be when your chin hits the bar. As above, if you do them right, you'll see much better results!