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Field of a static magnetic dipole

A magnetic dipole is a closed circulation of electric current. A simple example of this is a single loop of wire with some constant current through ... more

Magnetic potential energy

The energy of a magnetic moment “m” in an externally produced magnetic field “B”. Is related to the distance between magnetic ... more

Seismic moment

Seismic moment is a quantity to measure the size of an earthquake and is proportional to the area of the rupture times the average slip that took place ... more

Rotational stiffness

The stiffness of a body is a measure of the resistance offered by an elastic body to deformation. A body have a rotational stiffness when it is in a ... more

Euler's pump and turbine equation

The Euler’s pump and turbine equations are most fundamental equations in the field of turbo-machinery. These equations govern the power, efficiencies and ... more

Worksheet 308

Astrology, that unlikely and vague pseudoscience, makes much of the position of the planets at the moment of one’s birth. The only known force a planet exerts on Earth is gravitational.

(a) Calculate the gravitational force exerted on a 4.20 kg baby by a 100 kg father 0.200 m away at birth (he is assisting, so he is close to the child).

(b) Calculate the force on the baby due to Jupiter if it is at its closest distance to Earth, some 6.29e+11 m away. How does the force of Jupiter on the baby compare to the force of the father on the baby?

Father’s gravitational force on the baby is:

Newton's law of universal gravitation

Jupiter’s gravitational force on the baby is:

Newton's law of universal gravitation

(c) What should be the father’s weight, so that he exerts the same force on the baby as that of Jupiter? **
**this section is not included in the Reference material

Newton's law of universal gravitation


Other objects in the room and the hospital building also exert similar gravitational forces. (Of course, there could be an unknown force acting, but scientists first need to be convinced that there is even an effect, much less that an unknown force causes it.)

Reference : OpenStax College,College Physics. OpenStax College. 21 June 2012.
Creative Commons License : http://creativecommons.org/licenses/by/3.0/

Dedicated to little Konstantinos

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

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
Creative Commons License : http://creativecommons.org/licenses/by-sa/3.0/us/

Pearson's moment coefficient of skewness

In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its ... more

Pearson's moment coefficient of kurtosis (excess kurtosis)

In probability theory and statistics, kurtosis is any measure of the “tailedness” of the probability distribution of a real-valued random ... more

Thermal Diffusivity

In heat transfer analysis, thermal diffusivity (usually denoted α but a, κ and D are also used) is the thermal conductivity divided by density and specific ... more

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