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theBEAST
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Homework Statement
Using work energy theorem, solve:
The Attempt at a Solution
The actual answer (3.11s) is exactly half of my answer. Does anyone know what I did wrong?
grzz said:Note that moment of inertia of a uniform disc about an axis through its centre and perpendicular to its plane is
[itex]\frac{1}{2}[/itex]MR[itex]^{2}[/itex].
There should be two factors of 1/2 - one from Iω2/2 for the KE and another from I=Mr2/2.theBEAST said:Yup! That is what I used I believe.
The Work Energy Theorem is a fundamental principle in physics that states that the work done on an object is equal to the change in its kinetic energy. In other words, the net work done on an object is equal to the change in its speed or direction of motion.
The Uniform Disc Problem is a specific application of the Work Energy Theorem that involves a uniform disc rolling down a slope. In this problem, the work done by the force of gravity on the disc is equal to the change in its kinetic energy, which can be used to solve for its final speed at the bottom of the slope.
A uniform disc is a disc-shaped object with a constant mass distribution throughout its entire volume. This means that all points on the disc have the same mass and density, resulting in a symmetrical shape.
The work done by a force on a uniform disc can be calculated using the formula W = Fd cosθ, where W is the work done, F is the applied force, d is the distance over which the force is applied, and θ is the angle between the force and the direction of motion of the disc.
The Work Energy Theorem and the Uniform Disc Problem can be applied to many real-life situations, such as a rolling ball on a flat surface, a car rolling down a hill, or a pendulum swinging back and forth. These principles are also used in engineering and design, such as in the construction of roller coasters and other amusement park rides.