Two questions about rotation of this line

In summary, rotation refers to the circular movement of an object around a fixed point or axis, measured in degrees or radians. Clockwise rotation is when an object turns in the same direction as the hands of a clock, while counterclockwise rotation is the opposite. The rate of rotation can be affected by factors such as distance, mass, and force, and can also impact an object's motion and stability.
  • #1
flyingpig
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Two questions about rotation of this "line"

Homework Statement




[tex]3x^2 - 2\sqrt{3}xy +y^2 = 1[/tex]

Homework Equations



[tex]x = x'\cos\alpha - y'\sin\alpha[/tex]
[tex]y = x'\sin\alpha + y'\cos\alpha[/tex]


The Attempt at a Solution



The discriminant test is

[tex]4(3) - 4(3)(1) = 0[/tex]

Supposed to be a parabola, instead we get lines.

One other thing

Supposed that in

[tex]cot2\alpha = \frac{A - C}{B}[/tex]

And then we get that [tex]\alpha < 0[/tex], can that happen? Can we rotate clockwise?
 
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  • #2


The OP is missing a problem statement. What is it that you are having problems with?
 

FAQ: Two questions about rotation of this line

What is rotation?

Rotation refers to the circular movement of an object around a fixed point or axis. It involves the object turning or spinning in a circular motion, causing it to face different directions.

How is rotation measured?

Rotation can be measured in degrees or radians. In degrees, rotation is measured on a scale of 0 to 360, with 0 indicating no rotation and 360 indicating a full rotation. In radians, rotation is measured on a scale of 0 to 2π, with 0 indicating no rotation and 2π indicating a full rotation.

What is the difference between clockwise and counterclockwise rotation?

Clockwise rotation is when an object turns in the same direction as the hands of a clock, from left to right. Counterclockwise rotation is when an object turns in the opposite direction of the hands of a clock, from right to left.

What factors affect the rate of rotation?

The rate of rotation can be affected by the distance between the object and the axis of rotation, the mass of the object, and the force applied to the object. The shape and size of the object can also affect its rate of rotation.

How does rotation affect the motion of an object?

Rotation can affect the motion of an object by changing its orientation and causing it to move in a circular or angular path. It can also affect the stability and balance of the object, depending on its shape and center of mass.

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