Av ΣΜ = = Linear Kinematics v = Ax At Angular Kinematics Linear Kinetics Angular Kinetics ΔΕ 0-0₁ W = = t-ti ΣΕ = ma Ια At tf-ti Δω wf-wi α = = F-At= t-ti m(v₁ - v₁) At t-ti w = w₁ + at p = mv A0 = W = f.d ā = = At v = v₁ + at = (0 +700) t Ax = 2 1 Ax = vot+at² = (w + wo) t 2 1 A0 = wot+at² Ep = mg(Ah) = mv2 M At I(wf-w₁) = H = Iw W = M.0 M = Fd₁ Iw² Ek 2 2 kx² k02 v² = v² + 2a(Ax) w² = w² + 2α(AO) Ek Xi+1-xi-1 V₁ = s = re 2h x-12x1 + x{+1 a₁ = V₁₂ = rw h² (v₁ sin 0)² Yapex = yi a₁ = ra 2g 1 = Σ mur? Ee = 2 P = Fv Ee = 2 P = Mw I = ICM +md² [=1 1 vz ar == w²r Other Kinetics y-y₁ = (v₁sin )t, +gt Other Kinematics r |aTotal = a² + a² Hsegment Hlocal + Hremote = ICOMSWs + mr²wg = FFT
During the last rotation, a hammer thrower maintains a constant acceleration of his hammer, from 28 m/s at the beginning of the rotation to 32 m/s at the time of release. a) If the radius of the hammer's rotations is 1.3 m, what is the total linear acceleration when the hammer has covered 3/4 of the last rotation?
1) Find the tangential acceleration of the hammer: m/s2
2) Find the tangential velocity after 3/4 of the final rotation: m/s. (Note, this is NOT just 3/4 of the way from 28 to 32 , because you travel further in a given time at higher speed.)
3) Find the radial acceleration of the hammer after 3/4 of the final rotation: m/s2.
4) Find the total acceleration after 3/4 of the final rotation: m/s2.
b) How far will the throw go, if the initial launch angle is 41 degrees above the horizontal, 1.9 m above the ground.
1) Find the time-of-flight: s
2) Find the horizontal velocity: m/s
3) Find the horizontal distance: m.
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