At one instant, force Upper F Overscript right-arrow EndScripts equals 1.57 j Ov

Question

At one instant, force Upper F Overscript right-arrow EndScripts equals 1.57 j Overscript EndScripts N acts on a 0.517 kg object that has position vector r Overscript right-arrow EndScripts equals left-parenthesis 8.00 i Overscript EndScripts minus 8.00 k Overscript EndScripts right-parenthesis m and velocity vector v Overscript right-arrow EndScripts equals left-parenthesis negative 9.58 i Overscript EndScripts plus 9.58 k Overscript EndScripts right-parenthesis m divided by s. About the origin and in unit-vector notation, what are (a) the object's angular momentum and (b) the torque acting on the object?

Explanation / Answer

given

F = 1.57 j

m = 0.517 kg

r = 8 i - 8k

v = -9.58 i + 9.58 k

a) angular momentum, L = m*(r cross v)

= 0.517*((8i - 8k) cross (-9.58i + 9.58k))

= 0.517*(8*9.58(-j) + 8*9.58*(j) )

= (0i + 0j + 0k) kg.m^2/s

b) Torque, T = r cross F

= ((8i - 8k) cross 1.57 j )

= 8*1.57 k - 8*1.57*(-i)

= 12.6 i - 12.6 k

= (12.6 i + 0 j - 12.6 k ) N.m

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