chewytess said:Homework Statement
If the axis of rotation of a physical pendulum is placed closer to the COM, is the period of rotation longer? If it originally starts .5m from the COM the moves .3M from the COM the peroid shoud be longer right? I keep getting a longer period when the axis of roatation is placed closer to the COM, but it just deosnt seem right
Homework Equations
t=2pi*(sqrt(I/mgh)
I=(1/12)Ml^2
The Attempt at a Solution
mass is unknown
L= 1m
The period of a pendulum when the axis is moved closer to the center of mass (COM) is shorter compared to when the axis is at the top. This is because the distance between the pivot point and the center of mass is smaller, causing the pendulum to have a shorter arc length and thus a shorter period.
As the axis is moved closer to the COM, the period of the pendulum decreases. This is because the pendulum has a shorter arc length and therefore completes each swing in a shorter amount of time.
The main factor that affects the period of a pendulum when the axis is moved closer to the COM is the length of the pendulum. The shorter the pendulum length, the shorter the period. Other factors that may also have an impact include the mass and shape of the pendulum bob, as well as air resistance.
Yes, the period of a pendulum will change if the mass of the pendulum bob is increased while the axis is moved closer to the COM. This is because the increased mass will affect the pendulum's center of mass, altering the distance between the pivot point and the COM and ultimately changing the period.
If both the length and mass of the pendulum are adjusted while the axis is moved closer to the COM, the period of the pendulum will change. The period will decrease with a shorter length and increase with a longer length, and it will also change depending on the mass of the pendulum bob. The exact relationship between these factors can be described using the equation T = 2π√(I/mgd), where T is the period, I is the moment of inertia, m is the mass, g is the acceleration due to gravity, and d is the distance between the pivot point and the center of mass.