Calc based physics 1 homework help

AI Thread Summary
To solve the problem of a cart, circular hoop, and solid cylinder rolling down a 22-meter incline at a 22-degree angle, one must consider the moment of inertia and its effect on angular acceleration. The time taken for each object to reach the bottom can be determined by calculating their velocities, factoring in both translational and rotational motion. Objects with higher moments of inertia will roll down slower than those with lower moments. The moment of inertia for the hoop and cylinder is straightforward, but clarification is needed for the cart's moment of inertia. Understanding these principles is crucial for accurately solving the homework problem.
Nightrider519
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Homework Statement



A small cart, circular hoop and a solid cylinder of the same mass (5Kg) are allowed to roll down an incline plane. the length of the plane is 22 meters and the angle of incline is 22 degrees. Find the time it takes for each object to reach the bottom of the incline plane.

I am totally and utterly lost on how to even start the problem any help at all would be greatly appreciated thanks in advance
 
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I guess it has to see with the moment of inertia and angular acceleration.
It would be nice if you could find the velocity of the rolling objects (their center of mass' velocity) so that you could find out how much time they'll take to reach the bottom of the inclined plane.
 
how would the moment of inertia even apply to this problem
 
Think about it: if an object has a very huge moment of inertia, it will try to resist to roll. So it will go down slower than an object with a little moment of inertia.
 
k he moment of inertia for the hoop and cylinder is no problem but what about the shopping kart
 

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