Physics Urgent please help

posted by .

A physical pendulum consists of a body of mass contained in the xy-plane. The moment of inertia of the object about an axis perpendicular to the plane and passing through the object's center of mass is I_cm .

The object oscillates in the xy-plane about the point S a distance d from the center of mass as shown. What is the period of the pendulum for small angle oscillations where sin(theta )neraly =theta ?

  • Physics Urgent please help -

    I assume your mass is m and moment of inertia about the center of mass is Ic

    Then the total moment of inertia about the point S is I = (Ic + m d^2)

    If the xy plane is vertical and this is a physical pendulum hanging from point S then the gravity force down is mg at the center of mass. At angle theta, which I call Th, this has components mg cos theta along the rod and mg son Theta toward the center. The torque about S is therefore m g d sin Th trying to bring the pendulum back to center
    Then m g d sin Th = -I alpha
    where alpha is the angular acceleration
    If Th = x sin 2 pi f t (harmonic motion)
    then V =dTh/dt 2 pi f x cos 2 pi f t
    and alpha = dv/dt = -(2 pi f)^2 sin 2 pi f t
    which is -(2pif)^2 Th
    then
    m g d sin Th = I ( 2 pi f)^2 T
    now for small angles sin Th = Th in radians so
    m g d = I (2 pi f)^2
    or
    m g d = (Ic + m d^2)( 2 pi f)^2
    solve for f, the frequency
    then
    period = 1/f

  • Physics Urgent please help -

    Thank you very much Damon

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. physics (please check work)

    Four identical particles, each with mass m, are arranged in the x,y plane like a cross. They are connected by light sticks to form a rigid body. If m=2.0kg and a=1.0 m the rotational inertia of this array about the y axis is: work: …
  2. Inertia

    A thin, uniform rod is bent into a square of side length a. If the total mass is M , find the moment of inertia about an axis through the center and perpendicular to the plane of the square. Use the parallel-axis theorem. Express your …
  3. Physics

    An engineer has an odd-shaped 11.4 kg object and needs to find its rotational inertia about an axis through its center of mass. The object is supported on a wire stretched along the desired axis. The wire has a torsion constant κ …
  4. Physics

    A solid circular disk has a mass of 1.67 kg and a radius of 0.144 m. Each of three identical thin rods has a mass of 0.351 kg. The rods are attached perpendicularly to the plane of the disk at its outer edge to form a three-legged …
  5. physics

    What is the moment of inertia of a triangular plate ABC of mass M and side BC=a about an axis passing through A and perpendicular to the plane of the plate.
  6. Physics

    An object is formed by attaching a uniform, thin rod with a mass of mr = 6.54 kg and length L = 5.12 m to a uniform sphere with mass ms = 32.7 kg and radius R = 1.28 m. Note ms = 5mr and L = 4R. 1)What is the moment of inertia of the …
  7. physics

    An object is formed by attaching a uniform, thin rod with a mass of mr = 6.54 kg and length L = 5.12 m to a uniform sphere with mass ms = 32.7 kg and radius R = 1.28 m. Note ms = 5mr and L = 4R. 1)What is the moment of inertia of the …
  8. science

    Calculate the moment of inertia of a uniform disc of mass 200g and radius 5cm about an axis passing through its edge and perpendicular to its plane?
  9. Physics

    An engineer has an odd-shaped object of mass 16 kg and needs to find its rotational inertia about an axis through its center of mass. The object is supported on a wire along the desired axis. The wire has a torsion constant κ …
  10. Physics

    Since moment of inertia is a scalar quantity, a compound object made up of several objects joined together has a moment of inertia which is the scalar sum of the individual moments of inertia. A) A wooden cylinder has mass m and radius …

More Similar Questions