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Question
If the angular momentum of a planet is given by `vec"L" = 5"t"^2hat"i" - 6"t"hat"j" + 3hat"k"`. What is the torque experienced by the planet? Will the torque be in the same direction as that of the angular momentum?
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Solution
The torque experienced by the planet
`vecτ = ("d"vec"L")/("dt")` .........`["d"/"dt"("t"^"n") = "nt"^(("n" - 1))]`
= `"d"/"dt" (5"t"^2hat"i" - 6"t"hat"j" + 3hat"k")`
= `5"d"/"dt" ("t"^2)hat"i" - 6"d"/"dt" ("t")hat"j" + 3"d"/"dt" (hat"k")`
= `10"t"hat"i" - 6hat"j" + 0`
`vecτ = 10"t"hat"i" - 6hat"j"`
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