Question

A particle is located at the vector position r with arrow = (9.00î + 12.00ĵ) m and a force exerted on it is given by F with arrow = (7.00î + 6.00ĵ) N.

(a) What is the torque acting on the particle about the origin? τ = N · m

(b) Can there be another point about which the torque caused by this force on this particle will be in the opposite direction and half as large in magnitude? Yes or No ?

(c) Can there be more than one such point? Yes or No?

(d) Can such a point lie on the y axis? Yes or No?

(e) Can more than one such point lie on the y axis? Yes or No?

(f) Determine the position vector of one such point. (Give a point on the y axis.) r with arrow = m

Answer 1

torque T = (r x F)

T = (9i +12j) x (7i +6j)

T = 9*7 (i x i) + (9*6) *(i x j) + (12*7)*( j xi) + (12*6)(j xj)

i x i = j x j = 0   and

i x j = k and   j x i =- k

so

T = 63 k - 84 k

T = -21 k (N m)

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part B : yes,

from the principle of moments

T1 = T2

F1 r1 = F2 r 2

F2 r 2 = -(-21) k

(7i + 6j) * (rxi x ry j) = 21 k

7 ry k - 6 rx k = 21 k

7 ry - 6 rx = 21/2

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part C no , not more then one point is possible yes

part D   No

part E: no

part f:   rx = -6/7 and ry = 1

r = 6/7 i + j   is the location