To understand two different techniques for computing the torque on an object due

Question

To understand two different techniques for computing the torque on an object due to an applied force Imagine an object with a pivot point rho at the origin of the coordinate system shown (Figure 1). The force vector F^rightarrow lies in the xy plane, and this force of magnitude F acts on the object at a point in the xy plane. The vector r^rightarrow is the position vector relative to the pivot point p to the point where F^rightarrow is applied. The torque on the object due to the force F^rightarrow is equal to the cross product tau^rightarrow = r^rightarrow times F^rightarrow. When, as in this problem, the force vector and lever arm both lie in the xy plane of the paper of computer screen, only the Z component of torque is nonzero. When the torque vector is parallel to the Z axis (tau^rightarrow = tau k^rightarrow), it is easiest to find the magnitude and sign of the torque. In the figure, the dashed line extending from the force vector is called the line of action of F^rightarrow. The perpendicular r_m from the pivot point p to the line of action is called the moment arm of the force. What is the length, r_m, of the moment arm of the force F^rightarrow about point ? Express your answer in terms of r and theta. r_m = rsin(theta) Find the torque tau about rho due to F^rightarrow Your answer should correctly express both the magnitude and sign of tau. Express your answer in terms of r_m and F or in terms of F, theta, and F tau = r_m cos(theta)

Explanation / Answer

(G) rm = rsin

for finding rm we need to have perpendicular distance from point P to the line of action of force.

(H) torque = Frsin

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