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प्रश्न
Obtain an expression for the torque acting on a rotating body with constant angular acceleration. Hence state the dimensions and SI unit of torque.
Obtain an expression for the torque acting on a rotating body with constant angular acceleration.
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उत्तर
For m1, a1 = r1α
For m2, a2 = r2α
For mn, an = rnα
f1 = m1a1 = m1r1α
f2 = m2a2 = m2r2α
fn = mnrnα
Torque `(vectau) = vecr xx vecf`
= rfsin90°
τ = rf
`tau_1 = "r""f"_1 = "m"_1"r"_1^2alpha`
`tau_2 = "m"_2"r"_2^2alpha`
`tau_"n" = "m"_"n""r"_"n"^2alpha`
`tau = tau_1 + tau_2 + ... + tau_n`
Total Torgue on the body, `vectau_"net" = vectau_1 + vectau_2 + vectau_3 + ... vectau_"n"`
= `"m"_1"r"_1^2alpha + "m"_2"r"_2^2alpha + ..... + "m"_"n""r"_"n"^2alpha`
= `alpha("m"_1"r"_1^2 + "m"_2"r"_2^2 + ..... + "m"_"n""r"_"n"^2)`
I = mr2
`vectau_"net" = ("I"_1 + "I"_2 + "I"_3 + ......"I"_n)alpha`
= `"I"alpha`
Unit: N.m
dimension: [ML2T-2]
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