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Routh's rule is a graphical technique used to determine the number of roots of a real, characteristic equation that lie in the right-half plane of the complex plane. It helps determine the stability of a control system by evaluating the roots of the characteristic equation based on the coefficients of the system's transfer function.
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What is routh's rule for finding out the moment of inertia an area?
Routh's rule is a method used to determine the product of inertia for a given area, not the moment of inertia. It involves integrating products of the area and its coordinates to find the moment about a certain axis. The final result depends on the choice of axes and the specific problem being analyzed.
State ane prove perpendicular axis theorem?
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.
What is the equation for inertia?
There are two laws about inertia. The First Law has no formula. It is just a statement that says "an object will continue at constant velocity ,or at rest, until a net force acts on it". This property that requires a force to change its state of motion (or rest) is called the object's "inertia". The Second Law is a formula that describes how an object will move when a net force acts on it. The formula is F = ma. Where, F, is the force and , a , is the objects acceleration. And , m , is the objects mass, which is a measure of the object's inertia. So you could write the formula as a = F/m and in this way you see if the object's mass (inertia) is increased then in order to get the same acceleration you must increase the force. These two laws describe how an object's inertia ,or mass, resists changes in its motion.
How do you calculate the moment force about the pivot?
To calculate the moment force about a pivot, you multiply the force applied by its distance from the pivot. The formula is: Moment force = Force × Distance. Make sure to consider the direction of the force and apply the right-hand rule for the vector direction.
What is the direction of the vector product when finding the direction of the vector product a x d?
The direction of the vector product a x d is perpendicular to both vectors a and d, following the right-hand rule.
What is routh's rule for finding out the moment of inertia an area?
Routh's rule is a method used to determine the product of inertia for a given area, not the moment of inertia. It involves integrating products of the area and its coordinates to find the moment about a certain axis. The final result depends on the choice of axes and the specific problem being analyzed.
State ane prove perpendicular axis theorem?
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.
What is the theory on bifilar suspension experiment using a meter rule suspended by a thread on it's two ends?
The bifilar suspension experiment is used to determine the unknown moment of inertia of a rigid body. By suspending the object from two different points and measuring the period of oscillation, the moment of inertia can be calculated using the formula for a physical pendulum. This experiment helps verify the parallel axis theorem and provides a practical way to determine moment of inertia experimentally.
What is the rule for finding the area of a rectangle?
Length times width.
What is a sustained objective?
The judge's finding that a rule of the court was broken
What is the 3 times circle rule?
The 3 times circle rule is a rule for finding the circumfrence of a circle. Basiclly, you multiply the diameter by 3.
What is the equation for inertia?
There are two laws about inertia. The First Law has no formula. It is just a statement that says "an object will continue at constant velocity ,or at rest, until a net force acts on it". This property that requires a force to change its state of motion (or rest) is called the object's "inertia". The Second Law is a formula that describes how an object will move when a net force acts on it. The formula is F = ma. Where, F, is the force and , a , is the objects acceleration. And , m , is the objects mass, which is a measure of the object's inertia. So you could write the formula as a = F/m and in this way you see if the object's mass (inertia) is increased then in order to get the same acceleration you must increase the force. These two laws describe how an object's inertia ,or mass, resists changes in its motion.
What is a rule for finding the number of diagnols for a polygon with N sides?
The rule is: 0.5*(N2-3N) = number of diagonals
What is the rule for finding the radius when you have diameter?
The radius is 1/2 of the diameter.
State the rule used for rounding decimals?
Finding the nearest decimal
What do the knights believe finding this treasure will do?
it will kill ther parents and they will rule.
What is a general rule for finding the value of something?
Have it appraised by a knowledgeable dealer.
