The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. In the case of a box sliding down an incline, the work done by gravity is equal to the change in kinetic energy of the box. By calculating the work done by gravity and equating it to the change in kinetic energy, one can determine the speed of the box at the bottom of the incline.
The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. By calculating the work done on an object as it moves against gravity, we can determine the maximum height it reaches by setting the object's kinetic energy to zero at that point.
To determine the moments of inertia for an object, one can use mathematical formulas or physical experiments. The moment of inertia depends on the shape and mass distribution of the object. Common methods for deriving moments of inertia include integration, parallel-axis theorem, and the perpendicular-axis theorem. These methods involve calculating the distribution of mass around an axis to determine how the object resists rotational motion.
In physics, the perpendicular axis theorem (or plane figure theorem) can be used to determine the moment of inertia of a rigid object that lies entirely within a plane, about an axis perpendicular to the plane, given the moments of inertia of the object about two perpendicular axes lying within the plane. The axes must all pass through a single point in the plane.Define perpendicular axes , , and (which meet at origin ) so that the body lies in the plane, and the axis is perpendicular to the plane of the body. Let Ix, Iy and Iz be moments of inertia about axis x, y, z respectively, the perpendicular axis theorem states that[1]This rule can be applied with the parallel axis theorem and the stretch rule to find moments of inertia for a variety of shapes.If a planar object (or prism, by the stretch rule) has rotational symmetry such that and are equal, then the perpendicular axes theorem provides the useful relationship:DerivationWorking in Cartesian co-ordinates, the moment of inertia of the planar body about the axis is given by[2]: On the plane, , so these two terms are the moments of inertia about the and axes respectively, giving the perpendicular axis theorem.
Impulse-momentum theorem
Impulse-momentum theorem
The Pythagorean Theorem allows the mathematician to determine the value of the hypotenuse. The converse of the Pythagorean Theorem manipulates the formula so that the mathematician can use the values to determine that if the triangle is a right triangle.
Any two angles of a triangle determine the third angle. As a result, the side angle angle theorem is equivalent to the angle side angle theorem.
ASA
SAS
in simplifying complex circuits and for different loads this theorem proven very useful
Binomial Theorem consists of formulas to determine variables. In pharmacy it can be used to calculate risks and costs of certain medications.
sss
They use it to determine altitude and ground distance.
SAS
yes
Pythagoras's Theorem is used to determine if a triangle is a right triangle or not.
in automatic control the nyquist theorem is used to determine if a system is stable or not. there is also something called the simplified nyguist theorem that says if the curve cuts the "x-axies" to the right of point (-1,0) then the system is stable, otherwise its not.