Problem 1.17 - MomentOfForce Force Length × = F L ⋅ = M...

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Problem 1.17 [Difficulty: 2] Given: Basic dimensions M, L, t and T. Find: Dimensional representation of quantities below, and typical units in SI and English systems. Solution: (a) Power Power Energy Time Force Distance × Time = = FL t = From Newton's 2nd law Force Mass Acceleration × = so F ML t 2 = Hence Power FL t = ML L t 2 t = ML 2 t 3 = kg m 2 s 3 slug ft 2 s 3 (b) Pressure Pressure Force Area = F L 2 = ML t 2 L 2 = M Lt 2 = kg ms 2 slug ft s 2 (c) Modulus of elasticity Pressure Force Area = F L 2 = ML t 2 L 2 = M Lt 2 = kg ms 2 slug ft s 2 (d) Angular velocity AngularVelocity Radians Time = 1 t = 1 s 1 s (e) Energy Energy Force Distance × = FL = ML L t 2 = ML 2 t 2 = kg m 2 s 2 slug ft 2 s 2 (f) Moment of a force
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Unformatted text preview: MomentOfForce Force Length × = F L ⋅ = M L ⋅ L ⋅ t 2 = M L 2 ⋅ t 2 = kg m 2 ⋅ s 2 slug ft 2 ⋅ s 2 (g) Momentum Momentum Mass Velocity × = M L t ⋅ = M L ⋅ t = kg m ⋅ s slug ft ⋅ s (h) Shear stress ShearStress Force Area = F L 2 = M L ⋅ t 2 L 2 ⋅ = M L t 2 ⋅ = kg m s 2 ⋅ slug ft s 2 ⋅ (i) Strain Strain LengthChange Length = L L = Dimensionless (j) Angular momentum AngularMomentum Momentum Distance × = M L ⋅ t L ⋅ = M L 2 ⋅ t = kg m 2 ⋅ s slugs ft 2 ⋅ s...
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