# Why do we add the spin angular velocity and orbital anglar velocity when asked to calculate total angular velocity of Gyroscope?

Normally when we talk of angular velocity we mean how the angle of a vector changes with time with respect to an origin.Thus the oribital angular velocity of gyroscope makes sense to me.However I find that we add another type of angular velocity -spin angular velocity- to find total angular velocity.This seems a bit ambiguious as this angular velocity is not due to change in angle about our origin about which we calculated the orbital angular velocioty.Thus adding both to get angular velocity seems confusing to me.

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Imagine yourself as the center post of the gyro and you lean 15 degrees to the right you have a bucket of water that you spin over your head.(this represents the spin of the gyro) As it spins you will see the angle of the bucket spinning and then have a friend estimate the angle

1. If you left the bucket at the same angle as you lean you might fall over so spin the bucket as if it were at the top of your head when you were standing upright. Success
2. Note: Hope this helps you see the angle of the spin.
3. You will notice over a point the spin will no longer keep you up, this is due to the speed of the spin and the mass you are spinning. Have fun but don't get hurt.

Who says Physics has to be boring.

Choose a point P on the periphery of your gyroscope and paint it with some color. Then, as the gyroscope rotates take photos and if possible, record the time of each picture. Let's name O the origin around which rotates your gyroscope. Now, using the pictures and the times recorded, calculate the change in time of the angle between the line OP and some fix direction in space that passes through the origin O.

I hope that it helps,

Sofia

It's as simple as adding the two vectors, the vector that determines the orbital rate relative to your reference frame and defined origin, and the vector that defines the spin angular velocity relative to the spin axis of your gyroscope. The two vectors are tip to tail connected and their sum is just the vector connecting the origin to the tip of the spin vector.