Showing posts from December, 2007

Improve math skills of your kids - Learn step-by-step arithmetic from Math games

Math: Unknown - Step-by-step math calculation game for iOS.

Math: Unknown is much more than a math game. It is a step-by-step math calculation game which will teach users how to calculate in the correct order rather than just asking only the final calculated results.

The app consists of four basic arithmetic operations which are addition, subtraction, multiplication and division. In order to get started, users who are new to arithmetic can learn from animated calculation guides showing step-by-step procedures of solving each type of operation. It is also helpful for experienced users as a quick reference.

Generally, addition and subtraction may be difficult for users who just start learning math especially when questions require carrying or borrowing (also called regrouping). The app helps users to visualize the process of carrying and borrowing in the way it will be done on paper. Once users understand how these operations work, they are ready to learn multiplication and division.

For most students, division is considered as the most difficult arithmetic operation to solve. It is a common area of struggle since it requires prior knowledge of both multiplication and subtraction. To help users understand division, the app uses long division to teach all calculation procedures. Relevant multiplication table will be shown beside the question. Users will have to pick a number from the table which go into the dividend. Multiplication of selected number and divisor is automatically calculated, but the users have to do subtraction and drop down the next digit themselves. Learning whole calculation processes will make them master it in no time.

Math: Unknown is a helpful app for students who seriously want to improve arithmetic calculation skills.


Joint Length
The longer the joint length, the greater the total elongation will occur in the bolt to produce the desired clamp load or preload. In design, if the joint length is increased, the potential loss of preload is decreased.

Joint Material
If the joint material is relatively stiff compared to the bolt material, it will compress less and therefore provide a less sensitive joint, less sensitive to loss of preload as a result of brinelling, relaxation and even loosening.

Thread Stripping Strength
Considering the material in which the threads will be tapped or the nut used, there must be sufficient engagement length to carry the load. Ideally, the length of thread engagement should be sufficient to break the fastener in tension. When a nut is used, the wall thickness of the nut as well as its length must be considered.
An estimate, a calculation or joint evaluation will be required to determine the tension loads to which the bolt and joint will be exp…

Elements of the Design Process

All design activities must do the following:
1) Know the “customers’ needs.”
2) Define the essential problems that must be solved to satisfy the needs.
3) Conceptualise the solution through synthesis, which involves the task of satisfying several different functional requirements using a set of inputs such as product design parameters within given constraints.
4) Analyse the proposed solution to establish its optimum conditions and parameter settings.
5) Check the resulting design solution to see if it meets the original customer needs.
Design proceeds from abstract and qualitative ideas to quantitative descriptions. It is an iterative process by nature: new information is generated with each step, and it is necessary to evaluate the results in terms of the preceding step. Thus, design involves a continuous interplay between the requirements the designer wants to achieve and how the designer wants to achieve these requirements.

Designers often find that a clear description of the design re…

Cam design

Classes of Cams

may, in general, be divided into two classes: uniform motion cams and accelerated motion cams. The uniform motion cam moves the follower at the same rate of speed from the beginning to the end of the stroke; but as the movement is started from zero to the full speed of the uniform motion and stops in the same abrupt way, there is a distinct shock at the beginning and end of the stroke, if the movement is at all rapid. In machinery working at a high rate of speed, therefore, it is important that cams are so constructed that sudden shocks are avoided when starting the motion or when reversing the direction of motion of the follower.Cams

The uniformly accelerated motion cam is suitable for moderate speeds, but it has the disadvantage of sudden changes in acceleration at the beginning, middle and end of the stroke. A cycloidal motion curve cam produces no abrupt changes in acceleration and is often used in high-speed machinery because it results in low noise, vibration and …


A flywheel is a mechanical device with a significant moment of inertia used as a storage device for rotational energy. Flywheels resist changes in their rotational speed, which helps steady the rotation of the shaft when a fluctuating torque is exerted on it by its power source such as that caused by a piston-based (reciprocating) engine, or when an intermittent load, such as the motion of a piston pump, is placed on it.

Flywheels can be used to produce very high power pulses for experiments, where drawing the power from the public network would produce unacceptable spikes. A small motor can accelerate the flywheel between the pulses.

Flywheels may be classified as balance wheels or as flywheel pulleys. The object of all flywheels is to equalize the energy exerted and the work done and thereby prevent excessive or sudden changes of speed. The permissible speed variation is an important factor in all flywheel designs. The allowable speed change varies considerably for different classes …

Rotary motion

In practice most machines involve rotary motion as well as linear motion. This could be such examples as electric motors, gears, pulleys and internal combustion engines. Therefore if we need to calculate how fast a machine will reach full speed (in other words calculate the acceleration of all its components) then we must consider rotary acceleration, and the associated torques, as well as linear acceleration. Fortunately Newton’s second law of motion applies equally well to rotary motion provided we use the correct version of the formula.

Suppose we are looking at the acceleration of a solid disc mounted on a shaft and rotated by a pull cord wrapped around its rim. We cannot use the conventional form of Newton’s second law, F = ma, because although there is a linear force being applied in the form of the tension in the cord, the acceleration is definitely not in a line. We therefore cannot identify an acceleration a in units of m/s2. Furthermore some of the mass of the disc is close t…

Newton’s second law of motion

Let us go back to the legend of Newton and the apple. From the work on statics we will find that the apple stays on the tree as long as the apple stalk is strong enough to support the weight of the apple. As the apple grows there will come a point when the weight is too great and so the stalk will break and the apple falls. The quantity that is being added to the apple as it grows is mass. Sometimes this is confused with weight but there have now been many examples of fruits and seeds being grown inside orbiting spacecraft where every object is weightless and would float if not anchored down.

Mass is the amount of matter in a body, measured in kilograms (kg).

The reason that the apple hangs downwards on the tree, and eventually falls downwards, is that there is a force of attraction between the earth and any object that is close to it. This is the gravitational force and is directed towards the centre of the earth. We experience this as a vertical, downward force. The apple is therefore…

Newton's law of motion

When Newton first published these laws back in the seventeenth century he caused a great deal of controversy. Even the top scientists and mathematicians of the day found difficulty in understanding what he was getting at and hardly anyone could follow his reasoning. Today we have little difficulty with the topic because we are familiar with concepts such as gravity and acceleration from watching astronauts floating around in space or satellites orbiting the earth. We can even experience them for ourselves directly on the roller coaster rides at amusement parks.

Newton lived in the second half of the seventeenth century and was born into a well-to-do family in Lincolnshire. He proved to be a genius at a very early age and was appointed to a Professorship at Cambridge University at the remarkably young age of 21. He spent his time investigating such things as astronomy, optics and heat, but the thing for which he is best remembered is his work on gravity and the laws of motion. For this…