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A cylindrical can filled with corned beef and an identical can filled with apple juice both roll down an incline. Compare their angular and linear accelerations. Explain the difference.

A cylindrical can filled with corned beef and an identical can filled with apple juice both roll down an incline. Compare their angular and linear accelerations. Explain the difference.

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
7 years ago
The cylinder filled with corned beef and apple juice are identical therefore the mass of the corned beef and the apple juice will account for the rotational inertia of each.
The apple juice is lighter than the corned beef, therefore the cylinder containing the corned beef has larger rotational inertia relative to the cylinder containing apple juice. This allows the cylinder with apple juice to make more number of revolutions per second relative to the cylinder containing beef.
Therefore the angular acceleration of the cylinder containing apple juice would be greater relatively.
From the relation, one can deduce that the linear acceleration of the cylinder is equal to the angular acceleration for a radius R .
236-2168_1.PNG
Here a is the angular acceleration of the cylinder, R is the radius and the a is the linear tangential acceleration.
The cylinders are identical, therefore they have the same radius, and the cylinder with larger angular acceleration will have larger linear acceleration, which in this case is the cylinder filled with apple juice.

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