Rotating coordinate system, velocity

In summary, the conversation discusses two coordinate systems that coincide at time t=0, one of which is rotating about the z axis with an angular velocity given by ω = tk = tk0. The position vector in the rotating frame is expressed as r0 (t) = (t + 1) i0 + t^2 j0, and in order to find v0, the unit vectors must be differentiated as well.
  • #1
lemonsare
3
0

Homework Statement



Two coordinate systems xyz (…fixed) and x0y0z0 (moving) coincide at time t = 0.
The moving system is rotating about the …fixed z axis, which coincides with z0 axis. The angular velocity is given by ω = tk = tk0. The position vector as measured in the rotational frame is equal to
r0 (t) = (t + 1) i0 + t^2 j0:
1. Using the rotating frame …find v0.

Homework Equations



ω = tk = tk0
r0 (t) = (t + 1) i0 + t^2 j0

The Attempt at a Solution



So i know to find v0, i cannot just differentiate r0. but i am stuck.
 
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  • #2
Welcome to PF;
v0 is the velocity in the rotating reference frame?
r0 is the position in the rotating frame wrt time?

You also need to differentiate the unit vectors.
See: http://home.comcast.net/~szemengtan/ClassicalMechanics/SingleParticle.pdf
section 1.8 (p15)
 
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1. What is a rotating coordinate system?

A rotating coordinate system is a mathematical concept used to describe the position and motion of objects in space. It consists of a set of axes that rotate along with a moving object, allowing for a more accurate representation of its movement.

2. How is velocity calculated in a rotating coordinate system?

Velocity in a rotating coordinate system is calculated using the law of vector addition. This means that the velocity of an object is determined by adding its linear velocity (in a straight line) to its angular velocity (caused by rotation).

3. What is the Coriolis effect in a rotating coordinate system?

The Coriolis effect is a phenomenon that occurs in a rotating coordinate system, where objects moving in a straight line appear to curve due to the rotation of the coordinate system. This effect is commonly observed in weather patterns and ocean currents.

4. How does a rotating coordinate system affect Newton's laws of motion?

In a rotating coordinate system, Newton's laws of motion still apply, but they must be modified to account for the effects of rotation. This means that the equations used to describe motion will be more complex and may involve additional terms.

5. What are some real-life applications of a rotating coordinate system?

A rotating coordinate system is used in many fields, such as aerospace engineering, navigation, and meteorology. It is essential for accurately predicting the movement of objects and understanding complex natural phenomena, such as the Earth's weather patterns.

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