Problem 15: Long Problem 2 Consider a long rod pivoted at one end, laying on a horizontal frictionless table, as shown in the diagram. The bar has a non-uniform linear mass density given by: (x) = Ax + B, where A and B are positive constants and x =0 at the pivot. The total length of the bar is L. Pivot 3L/4 +z is out of the page +x (a) What is the moment of inertia of the bar? State your answer in terms of L, A, and B. (b) Say that a constant force F is applied at a distance 3L/4 from the pivot, at the direction shown in the diagram. What is the angular acceleration of the bar while this force acts? Give both the magnitude and the vector direction of the angular acceleration as this torque acts. Express your answer in terms of L, A, B, F, and o, and use the axes shown for stating the vector direction.
Problem 15: Long Problem 2 Consider a long rod pivoted at one end, laying on a horizontal frictionless table, as shown in the diagram. The bar has a non-uniform linear mass density given by: (x) = Ax + B, where A and B are positive constants and x =0 at the pivot. The total length of the bar is L. Pivot 3L/4 +z is out of the page +x (a) What is the moment of inertia of the bar? State your answer in terms of L, A, and B. (b) Say that a constant force F is applied at a distance 3L/4 from the pivot, at the direction shown in the diagram. What is the angular acceleration of the bar while this force acts? Give both the magnitude and the vector direction of the angular acceleration as this torque acts. Express your answer in terms of L, A, B, F, and o, and use the axes shown for stating the vector direction.
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Transcribed Image Text:Problem 15: Long Problem 2
Consider a long rod pivoted at one end, laying on a horizontal frictionless table, as
shown in the diagram. The bar has a non-uniform linear mass density given by:
2(x) = Ax? + B,
where A and B are positive constants and x =0 at the pivot. The total length of the
Pivot,
3L/4
bar is L.
+z is out of
the page
+x
(a) What is the moment of inertia of the bar? State your answer in terms of L, A, and B.
(b) Say that a constant force F is applied at a distance 3L/4 from the pivot, at the direction shown in the diagram. What is the angular acceleration
of the bar while this force acts? Give both the magnitude and the vector direction of the angular acceleration as this torque acts. Express your
answer in terms of L, A, B, F, and p, and use the axes shown for stating the vector direction.
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