When the angular velocity changes during a particular time| we say that ...

When the angular velocity changes during a particular time| we say that the body has angular acceleration which depends on such change in the angular velocity. The average angular acceleration using the initial angular velocity and the final angular velocities :

We have studied the linear motion under the influence of a constant ...

We have studied the linear motion under the influence of a constant acceleration and found the necessary laws for that| but now we know we have the angular velocity and angular acceleration. Is it possible to find similar equations to study the angle of movement under the influence of a Constant velocity. There are great similarities between the linear and rotational movements|

The external force acting on the body| which makes it move around ...

The external force acting on the body| which makes it move around the axis of rotation is known as known “torque”. It depends on the impact of the force on a point at which the body moves a rotational motion around a center so that the distance between the rotation center and the impact point is known as arm of torque

Since the torque occurs due to influence of external force F on ...

Since the torque occurs due to influence of external force F on an object of mass m| where the object will have a rotation motion around a rotational axis| thus we write the following:

The units of measurement are a fundamental part of physical quantities and ...

The units of measurement are a fundamental part of physical quantities and it required to define this quantity. The standard unit for a particular physical quantity is only valid for that quantity.

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2-1 Motion In this chapter we will examine the motion in one ...

2-1 Motion In this chapter we will examine the motion in one direction| which is the basic for understanding the motion in general| and during this study we will not studying the acting force (causing) the motion| which will be studied later in chapter five and six which explains Newton's laws and its applications. Our goal now is to understand the motion in one dimension| to reach that we need to define some physical quantities| such as the displacement of motion| speed and acceleration. At the last section of this chapter we will study the free fall and how to solve its problems.

Instantaneous velocities can be defined as the velocity of an object at ...

Instantaneous velocities can be defined as the velocity of an object at instant time. If we want to know the velocity of an object at a certain time and the position| we have to take limit of the average velocity when the time approaches zero.

When the velocity of an object changes| it means there are changes ...

When the velocity of an object changes| it means there are changes in the magnitude| or changes in the direction| or changes in both the direction and magnitude at the same time. In this case it is called that the object is moving with an average acceleration. Let us assume that υf and υi are the changes in the velocity and tf and ti are the changes in the time. Therefore average acceleration will be defined as:

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The instantaneous acceleration is measuring the acceleration at any particular instant time ...

The instantaneous acceleration is measuring the acceleration at any particular instant time during its motion| to be able to do that the object must be moving with a variable velocity. When the time interval t got smaller and smaller till approaches zero| the average acceleration will be known as the instantaneous acceleration at instant time| this means we need to take the derivative of the equation

When an object moves with a changing velocity with the time| we ...

When an object moves with a changing velocity with the time| we can say the object has acceleration. There are three deferent definitions of the acceleration:

Now studying the motion in one dimension| it will be the (x) ...

Now studying the motion in one dimension| it will be the (x) direction and the study of the motion in one direction and facilitate the study in two or three (which we will study later). Let us take the acceleration in the x- direction; we find that the average velocity and instantaneous acceleration they are equal if the acceleration is constant.

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The vector is represented by the symbol. The vector usually represents the ...

The vector is represented by the symbol. The vector usually represents the straight line between the two points (ab) as shown in Figure . The vector can be represented graphically be an angle with the x-axis and a magnitude (i.e. its length) as in the following figure.

The vector is represented by the symbol . The vector usually represents ...

The vector is represented by the symbol . The vector usually represents the straight line between the two points (ab) as shown in Figure (3-1) The vector can be represented graphically be an angle with the x-axis and a magnitude (i.e. its length) as in the following figure.

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Analytical method to add vectors is a way of representing a vector ...

Analytical method to add vectors is a way of representing a vector in to two component one in the x-axis and the anther in the y-axis| this happened as follow: If we have a vector A which make an angle Ө with the x-axis and its represented by the OP which makes the angle Ө as mentioned before. To find the x- and y- components of the vector| we make projections on the x-axis and y-axis to find Ax and Ay| as shown in the figure below. From the triangle shape therefore the two components will be as:

Vectors are not get added| subtracted| multiplied or even divided by the ...

Vectors are not get added| subtracted| multiplied or even divided by the traditional methods. One can only add two vectors of the same physical quantity. This mean that you can add vectors of displacement but you cannot add vector of displacement to a vector of velocity they must be the same physical quantity.

Vectors are not get added| subtracted| multiplied or even divided by the ...

Vectors are not get added| subtracted| multiplied or even divided by the traditional methods. One can only add two vectors of the same physical quantity. This mean that you can add vectors of displacement but you cannot add vector of displacement to a vector of velocity they must be the same physical quantity.

Vectors cannot be added | subtracted| multiplied or even divided by the ...

Vectors cannot be added | subtracted| multiplied or even divided by the traditional methods. One can only add two vectors of the same physical quantity. This mean that you can add vectors of displacement but you cannot add vector of displacement to a vector of velocity they must be the same physical quantity.

A vector whose magnitude is one in a particular direction is called ...

A vector whose magnitude is one in a particular direction is called a unit vector. It is used to represent the direction of that vector. At the time of writing vectors in three dimensions| we find it difficult to express in terms of vectors without identify their direction| A unit vector for Ax | Ay | Az are i | j | k | respectively| and they have a value of one (As shown in Figure (3-4)).

The absolute value of vector can be found if it has been ...

The absolute value of vector can be found if it has been measured experimentally or it is given in the Cartesian coordinates in the form of x| y| z. In this case the vector absolute value is calculated by taking the square root of the values of

Multiplying a vector A is multiplied by number “n” "n" of any ...

Multiplying a vector A is multiplied by number “n” "n" of any measurement value| such as if a vector A multiply by number “n”| the result will be a new vector B (nA=B)| this vector B will have the same direction as vector A but with different value. Consider a vector A equals 4 unit and one want to multiply it by a number 3| the resultant will be 3A = (3) (4) = 12. The value of the new vector is 12 unit with the same direction.

product means that a vector multiply with another vector but the result ...

product means that a vector multiply with another vector but the result will be numerical value that does not have any direction at all. The value of A.B for the two vectors AB| one can be calculated it as follow

1- The cross product is not commutative: AB= - BA= - C ...

1- The cross product is not commutative: AB= - BA= - C 2- If A and B are perpendicular to each other then Ө=900| this mean that sin90=1. This will give the maximum value of the cross product. AB= BA In the case the unit vector is multiplied by another unit vector(all unit vectors are perpendicular to each other) therefore the result will be:

The cross product symbolizes the product of two vectors A and B ...

The cross product symbolizes the product of two vectors A and B and it’s written as (A B). It must be noted the importance of arrangement in this type of vectors| and know which way the angle between the two vectors can be calculated. The result “C” of the multiplication is a new vector perpendicular to the two vectors A and B| and the direction of “C” is can be determined by applying the right hand law (or called a spiral).

3-6 Exercises 1 headed north through a distance of 40 km and ...

3-6 Exercises 1 headed north through a distance of 40 km and then make a move by an angle of 30o to the north-west through a distance of 50 km. Calculate the total displacement made by the train? - A train moves in the direction of east by distance of 50 km and then

We know that the free fall is the study of an objects ...

We know that the free fall is the study of an objects falling under the influence of gravity (with the neglect of air resistance). The distance of falling is small compared to the radius of the earth| the acceleration assumes to be constant. Because of the absence of air resistance| so we can apply all the previous laws for motion in straight line| noting that the movement in the direction (y) and the acceleration of a negative gravity (a =-g=- 9.8 m/s2) into the previous five laws as follows:

When one describe the motion of an object in a plane by ...

When one describe the motion of an object in a plane by using Cartesian Coordinates (x|y|z)| this is after one has identified the position of the object through the coordinates of its position (x1|y1|z1). After a certain period of time the object will move to another position (x2|y2|z2)| then one can find the velocity and the acceleration of object in these coordinates as follows:

The word projectile indicates that the object is moving in a curve ...

The word projectile indicates that the object is moving in a curve and not in a straight line as we studied in chapter two. For the projectile motion we will study same cases as: missile fired from ship| dropping a bomb from an aircraft as in the following figures; a bomb from a canon over a hill| or a hunter shooting a monkey on tree as in the next two animations

Rotational motion is the systematic movement of the body paints a circular ...

Rotational motion is the systematic movement of the body paints a circular track with a constant velocity| the velocity is a tangential to the orbit S and perpendicular to the radius R| the arc which represent the part S in the orbit :

The cross product symbolizes the product of two vectors A and B ...

The cross product symbolizes the product of two vectors A and B and it’s written as (A B). It must be noted the importance of arrangement in this type of vectors| and know which way the angle between the two vectors can be calculated. The result “C” of the multiplication is a new vector perpendicular to the two vectors A and B| and the direction of “C” is can be determined by applying the right hand law (or called a spiral).

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