Question

At any instant,`overset rarr(F) = (4.0 hatj)N` acts on a `0.25kg` object that has position vector `overset rarr(r ) = (2.0hati - 2.0 hatk)m` and velocity `overset rarr(upsilon) = (-5.0 hati + 5.0 hatk) m//s`. About the origin, what are angular momentum and torque acting on the object ?

Answer 1

Here, `overset rarr(F) = (4.0 hatj)N, m = 0.25 kg`
`overset rarr(r ) = (2.0 hati - 2.0 hatk)m`,
`overset rarr(upsilon) = (-5.0 hati + 5.0 hatk)m//s`
`overset rarr(L) = m (overset rarr(r ) xx overset rarr(upsilon)) = 0.25 (2.0 hati - 2.0 hatk) xx (-5.0 hati + 5.0 hatk)`
`= 0.25 |[hati, hatj, hatk],[2.0,0,-2.0],[-5.0,0,5.0]|`
`= 0.25[hati(0) - hatj (10 - 10) + hatk(0)] overset rarr(L) =` zero
`overset rarr(tau) = overset rarr(r ) xx overset rarr(F) = (2.0 hati - 2.0hatk) xx (4.0hatj)`
`= |[hati, hatj, hatk],[2.0,0,-2.0],[0,4.0,0]|`
`= hati (0+8) - hatj (0) + hatk (8 - 0)`
`= (8hati + 8hatk) N-m`