A force F_vec of magnitude F making an angle theta with the x axis is applied to

Question

A force F_vec of magnitude F making an angle theta 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_vec lies in the xy plane, and the four axes of rotation A, B, C, and D all lie perpendicular to the xy plane. A is at (0,0)
pt1) What is the torque tau_C about axis C due to F_vec? (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, theta, phi, pi, and/or other given coordinate data.
pt2)What is the torque tau_D about axis D due to F_vec? (D is the point located at a distance d from the origin and making an angle phi with the x axis.)
Express the torque about axis D in terms of F, theta, phi, pi, and/or other given coordinate data.

Explanation / Answer

1) Torque about C = F*(length of perpendicular drawn from (c,0) upon line of action of F) = F*c*sin(theta) tau_C = F*c*sin(theta) Alternatively, torque about C = |cross product of the vectors (c,0) and F| = F*c*sin(theta) 2) tau_D = |cross product of the vectors F and the position vector of the point D| i.e. tau_D = F*d*sin(|theta - phi|)

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