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Grade: 11

                        

Fig. shows a meter stick, half of which is wood and half of which is steel, that is pivoted at the wooden end at O. A force is applied to the steel end at a. In Fig. the stick is pivoted at the steel end at 0’ and the same force is applied at the wooden end at a'. Does one get the same angular acceleration in each case? If not, in which case is the angular acceleration greater?

5 years ago

Answers : (1)

Aditi Chauhan
askIITians Faculty
396 Points
							The figure below shows the meter stick, half of which is wood on the left side, and half is steel on the right side.
236-787_1.PNG
Assume that the volume of the steel is the same as the volume of the wood, the material with larger density will have more mass. The density of steel is greater than the density of the wood, therefore the steel half of the stick is heavier than the wood half.
From the figure above, it can be seen that the steel is on the right hand side and is farther away from the axis of rotation passing from point O’ and perpendicular to rod. Therefore, the stick will have large rotational inertia and lower angular acceleration.
The figure below shows the meter stick, half of which is wood (on the right) and half is steel (on the right).

236-839_1.PNG
As stated above, the steel is heavier than wood, and in this case closer to the axis of rotation. Therefore, it will be relatively easier to rotate the stick as compared to the situation in part (a), and the angular acceleration of the stick will be greater.
5 years ago
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