A square plate with sides of length 4.0 m can rotate about an axle passing through its center of mass and perpendicular to the plate as shown in Figure P14.36. There are four forces acting on the plate at different points. The rotational inertia of the plate is 24 kg·m2. Is the plate in equilibrium?
FIGURE P14.36
Whether the plate is in equilibrium, if rotational inertia of the plate is
Answer to Problem 36PQ
Since net torque acting on the plate is zero, the pate is in equilibrium.
Explanation of Solution
Take right direction as
From figure P14.36, write the expression for the vector form of force of magnitude
Here,
Write the expression for the vector form of force of magnitude
Here,
Write the expression for the vector form of force of magnitude
Here,
The force of magnitude
Write the expression for the vector form of force of magnitude
Here,
Write the position vector of point where
Here,
Write the position vector of point where
Here,
Write the position vector of point where
Here,
Write the position vector of point where
Here,
Write general expression for
Here,
Write the expression for torque.
Here,
Write the general form of
Here,
Substitute (IX) and (XI) in equation (X) to get
Write the expression for the torque due to force
Here,
Write the expression for the torque due to force
Here,
Write the expression for the torque due to force
Here,
Write the expression for the torque due to force
Here,
Conclusion:
Substitute
Substitute
Substitute
Substitute
Add
Write the expression for net torque.
Substitute
This indicates that the system is in rotational equilibrium.
Therefore, the pate is in equilibrium.
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Chapter 14 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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