Whether you do weightlifting before or after an aerobic workout is up to you. Research hasn't definitively shown that one way is better than another.
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Consider the factors that fuel the debate about when to do weightlifting:
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Weightlifting can deplete the glycogen stores in your muscles. Glycogen stores provide you with energy for short-duration intense activity and longer duration endurance activity.
If you do weightlifting first, you may find that you're too tired to complete a more intense aerobic workout.
- An aerobic workout can be a good warm-up for weightlifting. If you do your aerobic workout first, make sure that you're not too tired to lift weights with proper form. Poor weight training technique could increase the risk of injury.
- Oxygen use may be the same whether you do aerobic or resistance exercise first. Some studies found that the order of aerobic and resistance exercise during the same session doesn't affect how much oxygen is used or limit how much aerobic exercise can be done.
The bottom line about weightlifting first or second? If you want to include both weightlifting and aerobic exercise in the same workout, experiment to find what works best for you.
For instance, you could make either your aerobic workout or your weightlifting workout less intense. Or you could consider doing your weightlifting and aerobic workouts on different days.
Source: http://www.mayoclinic.org/healthy-living/fitness/expert-answers/weightlifting/faq-20057921