das Rad
wheel
A circular component that turns around an axle and enables vehicles to move.
Am Auto muss ein Rad gewechselt werden.
A wheel on the car needs to be changed.

wheel / bike
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wheel
A circular component that turns around an axle and enables vehicles to move.
Am Auto muss ein Rad gewechselt werden.
A wheel on the car needs to be changed.

'Rad' (wheel/bike) is a common component of compound words for things that have wheels or are round. Examples include 'Fahrrad' (bicycle), 'Motorrad' (motorcycle), 'Windrad' (wind turbine/pinwheel), or 'Zahnrad' (gear/cogwheel).
Das Windrad auf dem Hügel dreht sich langsam.
The wind turbine on the hill is turning slowly.
You can tell from context whether 'Rad' means a wheel (m01) or a bicycle (m02). If people are talking about cars or mechanics, it usually means the wheel. If they are talking about leisure time or the way to work, it often means the bicycle.
In der Werkstatt wurde das vordere Rad des Autos demontiert.
In the workshop, the front wheel of the car was removed.
When 'Rad' is used as a short form for 'Fahrrad' (bicycle), it very often appears in the fixed phrase 'mit dem Rad fahren' (to go by bike/ride a bike). The preposition 'mit' is typical here.
Am Wochenende fahren wir oft mit dem Rad an den See.
On weekends, we often ride our bikes to the lake.
The gymnastic exercise 'Rad schlagen' (to do a cartwheel) is a fixed expression. The verb is always 'schlagen'. You can say 'ein Rad schlagen', but not 'machen' or 'tun'.
Im Turnunterricht haben wir gelernt, ein Rad zu schlagen.
In gymnastics class, we learned to do a cartwheel.
The idiom 'am Rad drehen' (to go crazy) is a fixed unit and means to lose control. The person who is overreacting is the subject of the sentence.
Wegen des ganzen Stresses hatte er das Gefühl, bald am Rad zu drehen.
Because of all the stress, he felt like he was about to go crazy.
bridge
'die Brücke' and 'das Rad' can both refer to gymnastics exercises. In a 'Brücke', you bend your body backward and stand on your hands and feet, so that an arch is formed. In 'ein Rad schlagen' (to do a cartwheel), you move sideways over your hands and feet, almost like a turning wheel. The words can be confused because both appear in PE class or gymnastics. The movement is important: the bridge is more of a bent posture, while the cartwheel is a sideways overturning movement.

In der Pause hat Jonas auf der Wiese ein Rad geschlagen.
During the break, Jonas did a cartwheel on the grass.
Beim Turnen hält Lisa die Brücke schon mehrere Sekunden.
In gymnastics, Lisa can already hold the bridge for several seconds.