A force F of magnitude F making an angle with the x axis is applied to a particl

Question

A force F  of magnitude F making an angle with the x axis is applied to a particle located along axis of rotation A, at Cartesian coordinates (0,0) in the figure. The vector F  lies in the xy plane, and the four axes of rotation A, B, C, and D all lie perpendicular to the xy plane. (Figure 1)

A particle is located at a vector position r  with respect to an axis of rotation (thus r  points from the axis to the point at which the particle is located). The magnitude of the torque about this axis due to a force F acting on the particle is given by

=rFsin()=(momentarm)F=rF,

where is the angle between r  and F , r is the magnitude of r , F is the magnitude of F , the component of r  that is perpendicualr to F  is the moment arm, and F is the component of the force that is perpendicular to r .

Sign convention: You will need to determine the sign by analyzing the direction of the rotation that the torque would tend to produce. Recall that negative torque about an axis corresponds to clockwise rotation.

In this problem, you must express the angle in the above equation in terms of , , and/or when entering your answers. Keep in mind that =180degrees and (/2)=90degrees .

Part A

What is the torque A about axis A due to the force F ?

Express the torque about axis A at Cartesian coordinates (0,0).

Part B

What is the torque B about axis B due to the force F ? (B is the point at Cartesian coordinates (0,b), located a distance b from the origin along the y axis.)

Express the torque about axis B in terms of F, , , , and/or other given coordinate data.

Part C

What is the torque C about axis C due to F ? (C is the point at Cartesian coordinates (c,0), a distance c along the x axis.)

Express the torque about axis C in terms of F, , , , and/or other given coordinate data.

Part D

What is the torque D about axis D due to F ? (D is the point located at a distance d from the origin and making an angle with the x axis.)

Express the torque about axis D in terms of F, , , , and/or other given coordinate data.

Explanation / Answer

partA

torque TA= 0*F*sin0 = 0

part B

torque TB = b*F*sin(pi/2-theta) = b*F*costheta

part(C)

torque Tc= -c*F*sintheta

part(D)

torque TD= -d*F*sin(phi-theta)

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