Tip 1: How to Find the Forces of Inertia
Tip 1: How to Find the Forces of Inertia
Inertia is a concept of conservationspeed of the body and the continuation of the movement of the body without affecting the external forces. For example, if any force pushes the ball away, it will continue to move this or that time after the impact of the force - this is the movement by inertia.
Instructions
1
Determine the force of inertia. The force of inertia is a quantity having a direction, or vector, it is equal to the mass m of a material point multiplied by its acceleration, but it is directed opposite to acceleration. If the problem is a curvilinear motion, decompose the inertia force into a tangent, or so-called tangential component (designation: Jt), which is directed opposite to the tangential acceleration (designation: wt), and also to the centrifugal component (designation: Jn), it is directed along the principal normal to the trajectory from the center of curvature.
2
Remember the formula: Jt = nwt, Jn = mv2 / r, where v is the speed of the given point, r is the radius of the circle of curvature represented in the task, the trajectory.
3
When studying the movement in relation to suchInertial reference system, the inertia force is usually introduced for the possibility (only formal) to compose equations of dynamics in the form of simple equations of statics (according to the principle of D "Alambert, Kinetostatika).
4
The concept of "force of inertia" is used in the studyrelative motion. In this case, the addition to the forces acting on the material point adds to the interaction with other bodies of the portable Jper and Coriolis Jkop of the Force of inertia, which makes it possible to compose the equations of motion of this point in a noninertial (or moving) reference system in exactly the same way as in the inertial ( motionless).
Tip 2: How to find the moment of inertia about the axis
The moment of inertia of a body or system of material points relative to the axis is determined by the general rule for the moment of inertia of a material point with respect to some other point or coordinate system.
You will need
- A textbook on physics, a sheet of paper, a pencil.
Instructions
1
Read the general definition in the physics textbookthe moment of inertia of a material point with respect to any coordinate system or other point. As is known, this quantity is determined by the product of the mass of a given material point by the square of the distance from a given point, the moment of inertia of which is determined, to the origin of the coordinate system or to the point about which the moment of inertia is determined.
2
Note that in the case wherethere are several material points, the moment of inertia of the whole system of material points is determined almost in the same way. Thus, in order to calculate the moment of inertia of a system of material points with respect to a coordinate system, it is necessary to sum all the products of the masses of the points of the system by the squares of distances from these points to the common origin of the coordinate system.
3
Note that in the event that instead of a point,If you calculate the moment of inertia, consider any axis, then the rule for calculating the moment of inertia is practically unchanged. The only difference is how the distance from the material points of the system is determined.
4
Draw a line on the sheet of paper,representing the axis in question. Next to the line on the right and left side, put a few fat points, they will represent material points. Draw perpendiculars from the given points to the axis line, without intersecting it. The segments that you get are actually normals to the axis line, and correspond to those distances that are used to calculate the moment of inertia relative to the axis. Of course, your drawing demonstrates a two-dimensional problem, but in the case of a three-dimensional situation, the solution will be similar if perpendiculars are drawn in three-dimensional space.
5
Remember from the course started analysis that whentransition from a set of discrete points to a continuous distribution of them, it is necessary to move from summation over points to integration. The same applies to situations where you need to calculate the moment of inertia about the axis of a body, not the system of material points. In this case, summation over points becomes integration over the whole body with intervals of integration determined by the boundaries of the body. The mass of each point must be represented as the product of the point density by the volume differential. The volume differential itself is divided into a product of differentials of coordinates, along which integration is carried out.
Tip 3: How to solve the problem without x
When solving differential equations, it is not alwaysThe argument x (or time t in physical tasks) is explicitly available. Nevertheless, this is a simplified special case of specifying a differential equation, which often facilitates the search for its integral.
Instructions
1
Consider the physical task, leading to a differential equation, inwhich does not have the argument t. This is the problem of oscillations of a mathematical pendulum of mass m suspended on threads of length r in the vertical plane. It is required to find the equation of motion of the pendulum if at the initial moment the pendulum was stationary and deviated from the equilibrium state by an angle α. Resistance forces should be neglected (see Fig. 1a).
2
Decision. A mathematical pendulum is a material point suspended on a weightless and inextensible thread at the point O. Two forces act on the point: the gravitational force G = mg and the tension force of the filament N. Both these forces lie in the vertical plane. Therefore, to solve the problem, we can apply the equation of the rotational motion of a point about the horizontal axis passing through the point O. The equation for the rotational motion of the body has the form shown in Fig. 1b. In this case, I is the moment of inertia of the material point; j - angle of rotation of the filament along with a point, counted from the vertical axis counterclockwise; M is the moment of forces applied to the material point.
3
Calculate these quantities. I = mr ^ 2, M = M (G) + M (N). But M (N) = 0, since the line of action of the force passes through the point O. M (G) = - mgrsinj. The sign "-" means that the moment of force is directed in the opposite direction to the movement. Substitute the moment of inertia and the moment of force into the equation of motion and get the equation shown in Fig. 1c. By reducing the mass, a relationship arises (see Figure 1d). There is no argument t.
4
In the general case, the differential equation of the nthof order not having x and solved with respect to the highest derivative y ^ (n) = f (y, y ', y' ', ..., y ^ (n-1)). For the second order, this is y '' = f (y, y '). Solve it by substituting y '= z = z (y). Since for a complex function dz / dx = (dz / dy) (dy / dx), then y '' = z'z. This leads to the first-order equation z'z = f (y, z). Solve it in any of the ways known to you and get z = φ (y, C1). As a result, we have obtained dy / dx = φ (y, C1), ∫dy / φ (x, C1) = x + C2. Here C1 and C2 are arbitrary constants.
5
The specific decision depends on the type ofdifferential equation of the first order. So, if this is an equation with separable variables, then it is solved directly. If this equation is homogeneous with respect to y, then for the solution apply the substitution u (y) = z / y. For the linear equation z = u (y) * v (y).
Tip 4: What are the inertial coils for fishing
An inertial coil is a device thatis accompanied by unwinding the line under the action of inertia force, caused by the lure when casting. It attracts fishermen with its high sensitivity and simplicity.
"Nevskaya" - this is the most popular coil amongfishermen. It has an attractive appearance, and is also very easy to maintain. This coil has a low price. The drum weight is 90 g. It accommodates up to 100 m of fishing line with a diameter of 0.7 mm. With the help of a screw with a lock nut, the end runout is regulated. In the coil there is an adjustable trolley. It is able to reduce the speed of rotation of the drum, in order to save the angler from unraveling the line. Strong tightening can dramatically reduce the casting distance, it is best to brake the drum with your finger.
"Kiev" - a coil, which is made onaxis and is equipped with an automatic retarder. The diameter of the winding is 100 mm. The drum can hold 100 m of fishing line with a diameter of 0.6 mm. The coil has a ratchet brake. Autotremosis is advisable to use only when catching heavy spoon baits, and for medium and light baits the casting distance is reduced. 
"Obolon" is a coil produced withrotary drum by 90 °. To make it work as an inertial coil, you need to install the drum across the rod. The diameter of the winding is 70 mm and is placed 100 m of fishing line with a diameter of 0.4 mm. For spinning it is of little use, it is recommended to use for bottom fishing rods.
