A square plate with sides 2.0 m in length can rotate around an axle passing through its center of mass (CM) and perpendicular to its surface (Fig. P12.53). There are four forces acting on the plate at different points. The rotational inertia of the plate is 24 kg · m2. Use the values given in the figure to answer the following questions. a. What is the net torque acting on the plate? b. What is the
FIGURE P12.53
Problems 53 and 54.
(a)
The net torque acting on the plate.
Answer to Problem 53PQ
The net torque acting on the plate is
Explanation of Solution
Write the expression for the net torque on the plate.
Here,
Write the expression for the torque acting on an object in the cross product form.
Here,
Equation (II) can be solved as,
Conclusion:
For each forces
The diagonal of the square is the square root of the sum of the squares of the two sides of the square which can be found that,
For the torque due to force
The angle between the moment arm and the force is
Substitute
Therefore, the net torque acting on the plate is
(b)
The angular acceleration of the plate.
Answer to Problem 53PQ
The angular acceleration of the plate is
Explanation of Solution
Write the expression for the total torque in terms of rotational inertia.
Here,
Rearrange equation (IV),
Conclusion:
Substitute
Therefore, the angular acceleration of the plate is
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Chapter 12 Solutions
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