What is the moment of inertia of the pendulum

In summary, the question asks for the moment of inertia of a pendulum with a solid sphere, bar, and block attached to it, each with a mass of 4 kg. The sphere has a radius of R, the bar attaches the block and sphere with a length of 2R, and the block has a center of mass R away from the end of the bar. Using the parallel axis theorem twice, the moment of inertia is calculated to be 124.6 r^2.
  • #1
dazedy
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Homework Statement


A pendulum constructed of a solid sphere, bar, and block, each with mass m=4 kg
The sphere has radius R, The bar attaches the block and sphere and has length 2R, and the block has a center of mass R away from the end of the bar. The axis of rotation is halfway between the top of the sphere and its center (R/2)
What is the moment of inertia of the pendulum (note: you will need to use the parallel axis theorem twice!)

Homework Equations


I = I(sphere) + I (bar) + I (block)
I(sphere) = (2mr^2)/5
I(bar) = (mL^2)/12
I(block) = mr^2 (treat as point mass bc you know center of gravity)
Parallel axis theorem: Iaxis = Icm + mr^2

The Attempt at a Solution


Should I simply solve for I, plugging in the equations above?

I = [(2mr^2)/5 + m(r/2)^2] + (m(2r)^2)+m(2.5r)^2 + m(4.5r)^2 = 124.6 r^2
 
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  • #2
Nevermind, figured the problem out.
 

What is the moment of inertia of the pendulum?

The moment of inertia of a pendulum is a measure of its resistance to rotational motion. It is a property of the pendulum that depends on its mass distribution and the distance between its pivot point and its center of mass.

How is the moment of inertia of a pendulum calculated?

The moment of inertia of a pendulum can be calculated using the formula I = m * L^2, where m is the mass of the pendulum and L is the distance between the pivot point and the center of mass. This formula assumes that the pendulum is a simple point mass attached to a weightless rod.

What factors affect the moment of inertia of a pendulum?

The moment of inertia of a pendulum is affected by its mass distribution, the distance between its pivot point and center of mass, and the shape of the pendulum. A pendulum with a larger mass or a longer distance between the pivot point and center of mass will have a larger moment of inertia.

Why is the moment of inertia important in understanding pendulum motion?

The moment of inertia plays a crucial role in understanding pendulum motion because it determines the period of the pendulum's oscillation. A higher moment of inertia will result in a longer period, while a lower moment of inertia will result in a shorter period.

How does the moment of inertia impact the stability of a pendulum?

The moment of inertia also affects the stability of a pendulum. A higher moment of inertia will result in a more stable pendulum, as it will require more energy to change the pendulum's direction of motion. On the other hand, a lower moment of inertia will result in a less stable pendulum, making it easier for external forces to alter its motion.

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