An educational film on physics, intended for students of specialized universities. The film examines the Theorem of Kinetic Momentum and its practical application in sports, space technologies, etc.
Space, starry sky.
Spacecraft.
A helicopter takes off.
Ballerinas on stage do a fouette.
A centrifugal regulator rotates.
A figure skater does spins on ice.
A cobblestone spins.
A formula for the kinetic moment relative to the center is derived on the cobblestone.
The sum of the kinetic moments of the material points of a system is called the kinetic moment of this system.
Formula for the kinetic moment of a system.
If the vector of the kinetic moment of a system is projected onto any axis, we obtain the kinetic moment of the system relative to this axis.
The same value is equal to the sum of the kinetic moments of all material points of the system relative to the axis.
A machine is working, a part is rotating, metal shavings are pouring out.
A cobblestone is rotating on a stand.
A solid body can be considered as a set of material points.
Summing over all points, we obtain the kinetic moment of the body relative to the axis of rotation.
It is equal to the product of the moment of inertia of the body and its angular velocity (a formula has been derived).
The disk is rotating.
The greater the moment of inertia of a body and the faster it rotates, the greater its kinetic moment.
Large - hands launch a toy top (spinning top), the top spins.
Large - a person holds a grinding device in his hands, the disk of the device rotates.
A cylinder on a stick rotates.
The kinetic moment vector is both in length and in direction.
The time derivative of the kinetic moment of a system relative to a fixed center is equal to the principal moment of external forces - this is how the Theorem of Moments is formulated (a formula has been derived).
Large - hands launch a toy top (spinning top), the top rotates.
When the moment of external forces is directed perpendicular to the kinetic moment, its direction changes.
The cylinder on the stick rotates.
The kinetic moment of a rapidly rotating top can be considered to be directed along its axis.
Large - hands hold a cylinder on a stick (spinning top), this structure is attached to a rope.
A man launches a top in an inclined position, the top rotates on a rope.
The force of gravity creates a moment directed perpendicular to the axis of the top.
Close up - hands apply a triangle ruler to the structure, measure the angle.
The top rotates on a rope.
The moment of gravity changes the direction of the kinetic moment vector, therefore, the direction of the top axis will also change.
In the frame - a gyroscope device.
The rotor spins.
The direction of its axis remains unchanged.
A weight is suspended from the inner frame of the device.
The moment of gravity of the weight turns the gyroscope axis (the gyroscope begins to rotate).
The weight is rebalanced - and the direction of the moment changes (the gyroscope begins to move in the other direction).
From the Theorem on kinetic moment in particular it follows that for a body rotating about an axis, its angular acceleration depends on the moment of external forces and the moment of inertia of the body (a formula is derived).
Moment of inertia of bodies - formula.
A physics experiment with three bodies of the same mass but different shapes.
The bodies are set in rotation by applying equal moments.
When the weights fall, the disks rotate with different angular accelerations, since they have different moments of inertia.
After starting, the gyroscope rotates uniformly without the effect of external forces.
Its kinetic moment retains its module and direction.
Here we see the manifestation of the Law of Conservation of Kinetic Momentum.
If the main moment of external forces relative to some center is zero, then the kinetic moment of the system remains constant.
If the moment of external forces relative to some axis is zero, then the kinetic moment of the system relative to this axis is also a constant value.
The action of this law is demonstrated (using a physical experiment).
On a special installation, threads hold the weights in equilibrium.
The gravity forces of the weights are external forces acting on the system.
Their moment relative to the vertical axis is zero.
It is worth removing the thread - the weights will approach the axis of rotation.
The moment of inertia of the entire system has decreased, and the angular velocity has increased proportionally.
Figure skaters on ice make rotational movements - by changing the position of their arms and legs, the skater can also change the speed of rotation.
A ballerina on stage spins a fouette.
Physics, kinetic force, kinetic moment, fouetté, spinning top, gyroscope
A room, demonstrating a physical experiment (the law of conservation of kinetic momentum relative to the axis), a rotating platform chair is shown in the frame, a portrait of the mechanical scientist N. E. Zhukovsky hangs on the wall.
A man approaches the chair, sits on it, takes a wheel in his hands, spins it, and the platform chair begins to rotate in the opposite direction.
When the wheel axis is horizontal, the platform does not rotate.
If the axis of the rotating wheel is again placed vertically, the platform with the man begins to rotate again.
In all these cases, the kinetic moment of the system as a whole relative to the vertical axis remains equal to zero.
Animation insert - space, starry sky, solar system, planets, etc.
The plane perpendicular to the vector of the kinetic moment of the solar system is called the Laplace plane - the orbits of the planets are oriented relative to it.
Various devices, designs for physical experiments in mechanics and kinematics.
A man on a rotating platform with dumbbells - sometimes pressing them to himself, sometimes spreading his arms, depending on this, the platform sometimes speeds up the rotation, sometimes slows down.
Animated insert - an airplane in the sky, a spacecraft in orbit, gears and mechanisms are spinning.
A pole vaulter takes a run-up and jumps.
The animated figure shows that in the case of translational motion of a non-inertial system, the theorem is formulated as follows - the time derivative of the kinetic moment in relative motion is equal to the sum of the moments of all external forces applied to the system and the moment of the resultant force Фс of inertia of all particles in the system (a formula is derived).
The kinetic moment, the moment of force Фс are taken relative to the moving origin - point A. Physical experiment - a hand starts a pendulum.
The oscillation period of a pendulum installed on a stationary platform is determined by its length and the acceleration of gravity (a formula is derived).
If the platform of the pendulum moves upward with some acceleration, then it is advisable to calculate the period of oscillation of the pendulum using the theorem of moments for motion in a non-inertial frame of reference (a formula is derived).
In the latter case, the period of oscillation becomes shorter (two pendulums are compared).
When the platform is lowered with acceleration, the period of oscillation of the pendulum increases (a formula is derived).
During free fall, when the acceleration of the system is g, the pendulum does not oscillate.
The figure shows a space satellite (in section).
Animation insert - the satellite moves along the Earth's orbit.
The pendulum on the satellite can be in equilibrium in any position, since the acceleration of this satellite is equal to the force of gravity (a = g).
Animated figure - if we place the origin of moving coordinates at the center of mass of the system, that is, where the resultant of inertial forces is applied, then its moment will become equal to zero.
In this case, the theorem on the change in kinetic moment is formulated in the same way as if the center of mass were a fixed point (a formula is derived).
A diver stands on a diving board, prepares to jump, jumps (slow motion).
After the push, only gravity acts on the athlete (freeze frame of the jump).
Its moment relative to his center of mass is zero, so the kinetic moment of the body is constant.
Different frames with an athlete jumping from a diving board into the water.
By grouping his body relative to the axis of rotation, the athlete reduces his moment of inertia, as a result of which his angular velocity increases proportionally.
A female athlete jumps from a springboard into the water.
By straightening up, the athlete increases the moment of inertia of her body, and the angular velocity decreases.
A spacecraft in orbit can rotate with a small angular velocity for various reasons.
To stop the rotation, the spacecraft's jet microengines create a pair of forces, the moment of which is directed opposite to the rotation of the spacecraft and slows down its rotation.
Experiment with Zhukovsky's bench - the wheel and the platform rotate in opposite directions.
New experiment - the platform with a person rotates, and the wheel spins in the same direction.
In this case, the platform will stop or rotate in the opposite direction at the corresponding value of the angular velocity of the wheel.
The rotation of the spacecraft can also be controlled using flywheels installed on it.
A flywheel rotating around an axis parallel to the satellite axis causes the same dynamic effect.
A spacecraft in orbit.
A top is spinning.
A helicopter rises into the air.
An athlete jumps from a tower into the water.
A figure skater spins on ice.
An athlete does a high pole vault.
Animated insert - space, stars.
The picture shows an astronaut in outer space.
Physics, science, kinetic moment, law of conservation of kinetic momentum relative to the axis, Laplace plane, Theorem on the change of kinetic momentum, diver, space, spacecraft