What is the formula of theorem of parallel axis 2 points?
Ic = moment of inertia about the centre. M = mass of the body. h2 = square of the distance between the two axes.
When can we apply perpendicular axis theorem?
The Perpendicular Axis Theorem Ix+Iy=Iz only applies if z=0 for all points of the object – ie if the object is confined to the xy plane.
What is radius of gyration of compound pendulum?
Mathematically the radius of gyration is the root mean square distance of the object’s parts from either its center of mass or a given axis, depending on the relevant application. It is actually the perpendicular distance from point mass to the axis of rotation.
What is compound pendulum give an example?
A compound pendulum has an extended mass, like a swinging bar, and is free to oscillate about a horizontal axis. A special reversible compound pendulum called Kater’s pendulum is designed to measure the value of g, the acceleration of gravity.
What is the advantage of compound pendulum over simple pendulum?
The main difference between simple pendulum and compound pendulum is that, in a simple pendulum, the distance between the centre of gravity of the suspended body and the axis of suspension is large compared to the dimensions of the suspended body whereas, in a compound pendulum, the dimensions of the suspended body are …
Why is compound pendulum preferred?
This is due to an ideal simple pendulum cannot be realized underlaboratory condition whereas the compound pendulum is preferred for determination theacceleration due to gravity because it moves as one rigid body and the moment of inertia ofthe whole body is take into an account.
What are the disadvantages of simple pendulum over bar pendulum?
The limitations are (1) we cannot get a heavy point mass and so use a small metallic bob (2) we cannot get a massless , inextensible , torsionless , perfectly flexible fibre and so use a thin light string. (3) we cannot get a perfectly rigid support and so strong stable support is used to suspend the pendulum.
What are disadvantages of simple pendulum?
The drawbacks of simple pendulum are as follows: a) The simple pendulum can’t have a weightless, heavy point mass bob with inextensible string as we assumed. b) The motion of the bob is not strictly linear. c) The resistance and buoyancy of air affects the motion of the bob which is supposed to be negligible.
Can we interchange the centers of suspension and oscillations in a compound pendulum If yes then show it?
Interchangeability of centers of suspension and oscillation The time period about point of oscillation is same as the axis of suspension through S. Thus the centre of oscillation and oscillation are interchangeable.
Which is better simple or compound pendulum?
What are the advantages of compound pendulum?
This allows us to treat the mass as though it were a single point. In a compound pendulum, the distance between the centre of gravity of the swinging body and the axis of suspension is comparable to the dimensions of the body.
What are the applications of compound pendulum?
were then used to study the effects of varying the weight distribution, wheelbase, and incorporating a suspension. A third example of the compound pendulum method of measuring weight distribution is its application to sail- boats. The total weight of a sailboat has a major effect on its speed.
What is the center of gravity of compound pendulum?
In this condition, the mass of the bob is concentrated at the centre of gravity. When the dimension of the bob is not negligible in comparison to the distance from the axis of suspension to the centre of gravity, then the pendulum is called the compound pendulum.
How do you perform a compound pendulum experiment?
The compound bar pendulum AB is suspended by passing a knife edge through the first hole at the end A. The pendulum is pulled aside through a small angle and released, whereupon it oscillates in a vertical plane with a small amplitude. The time for 10 oscillations is measured.
Which shape of body can be considered as compound pendulum?
spherical
What is the time period of a compound pendulum at its Centre of gravity?
T=2π√Imgl. whereI=moment of inertia about the centre of the suspension,g=acceleration due to gravity , m=mass of the pendulaml=distance of the centre of the gravity from the centre of the suspension.