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Film temperature

In heat transfer and fluid dynamics, the film temperature is an approximation to the temperature of a fluid inside a convection boundary layer. It is ... more

Worksheet 334

In a video game design, a map shows the location of other characters relative to the player, who is situated at the origin, and the direction they are facing. A character currently shows on the map at coordinates (-3, 5). If the player rotates counterclockwise by 20 degrees, then the objects in the map will correspondingly rotate 20 degrees clockwise. Find the new coordinates of the character.

To rotate the position of the character, we can imagine it as a point on a circle, and we will change the angle of the point by 20 degrees. To do so, we first need to find the radius of this circle and the original angle.

Drawing a right triangle inside the circle, we can find the radius using the Pythagorean Theorem:

Pythagorean theorem (right triangle)

To find the angle, we need to decide first if we are going to find the acute angle of the triangle, the reference angle, or if we are going to find the angle measured in standard position. While either approach will work, in this case we will do the latter. By applying the cosine function and using our given information we get

Cosine function
Subtraction

While there are two angles that have this cosine value, the angle of 120.964 degrees is in the second quadrant as desired, so it is the angle we were looking for.

Rotating the point clockwise by 20 degrees, the angle of the point will decrease to 100.964 degrees. We can then evaluate the coordinates of the rotated point

For x axis:

Cosine function

For y axis:

Sine function

The coordinates of the character on the rotated map will be (-1.109, 5.725)

Reference : PreCalculus: An Investigation of Functions,Edition 1.4 © 2014 David Lippman and Melonie Rasmussen
http://www.opentextbookstore.com/precalc/
Creative Commons License : http://creativecommons.org/licenses/by-sa/3.0/us/

Leadscrew Frictional Torque of the Thrust Collar

A leadscrew (or lead screw), also known as a power screw or translation screw, is a screw used as a linkage in a machine, to translate turning motion into ... more

Darcy friction factor - Blasius correlation with correction for curved or helically coiled tubes (Variable Rc)

In fluid dynamics, the Darcy friction factor ormulae are equations that allow the calculation of the Darcy friction factor, a dimensionless quantity used ... more

Torque to lower a load (by lead screw-related to the coefficient of friction))

A leadscrew (or lead screw), also known as a power screw or translation screw, is a screw used as a linkage in a machine, to translate turning motion into ... more

Torque to lift a load (by a lead screw - related to the coefficient of friction)

A leadscrew (or lead screw), also known as a power screw or translation screw, is a screw used as a linkage in a machine, to translate turning motion into ... more

Darcy friction factor - Blasius correlation with correction for curved or helically coiled tubes

In fluid dynamics, the Darcy friction factor formulae are equations that allow the calculation of the Darcy friction factor, a dimensionless quantity used ... more

Drift velocity in a current-carrying metallic conductor

The drift velocity is the average velocity that a particle, such as an electron, attains due to an electric field. In general, an electron will 'rattle ... more

Reduced specific volume

In thermodynamicsIn thermodynamics, the reduced properties of a fluid are a set of state variables normalized by the fluid’s state properties at its ... more

Hill equation

In biochemistry, the binding of a ligand to a macromolecule is often enhanced if there are already other ligands present on the same macromolecule (this is ... more

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