Question

A) a particle is located at r=(4.0i+3.5j+6.0k) meters has a force F=(6.5j-3.2k) Newtons acting on it. Find the torque with reference to the origin.

B) the origin of a coordinate system is at the center of a wheel which rotates in the xy plane about its axle which is the z axis. A force F=215N acts in the xy plane at a 33 degree angle to the x axis (33 degrees north of east) at the point x=28cm, y=33.5cm. Determine the magnitude and direction of the torque due to this force about the axis.

Answer 1

(A) r = (4.0i + 3.5j + 6.0k)

F= (6.5j - 3.2k)

Torque,

= i(- 3.2 x 3.5 - 6 x 6.5) - j(- 3.2 x 4 - 0) + k(4 x 6.5)

= - 50.2 i + 1.8 j + 26 k

(b) slope of the line m = tan = tan33 = 0.64941 and a point (28, 33.5)

Equation of line of action of fore vector

y - 33.5 = 0.64941(x - 28);

y = 0.64941 x + 15.32

0.64941 x - y + 15.32 = 0

perpendicular distance from the origin;

therefore,

torque,

215 x 9.2882 = 1996.956 N-cm