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Uniform solid sphere with dia 28cm and mass 2.5kg rolls without slipping on a horz surface at a constant speed of 2.0 m per s What is its rotational kineticenergy and total kinetic energy and ang mome?
Shawn8686
Sphere radius, R = (28 cm)/2 = 14 cm = 0.14 m
Speed, v = 2 m/s
Mass, M = 2.5 kg
Rotational KE = ½𝙸𝜔²
For solid sphere, the moment of inertia, 𝙸 = ⅖MR²
Rotational KE = ½(⅖MR²)(v/R)²
= ⅕Mv²
= ⅕(2.5 kg)(2 m/s)²
= 2 J
Total KE = Linear KE + Rot KE
Total KE = ½Mv² + ⅕Mv²
Total KE = (7/10)(Mv²)
Total KE = (7/10)(2.5 kg)(2 m/s)²
Total KE = 7 J
Angular momentum, 𝜔 = v/R = (2 m/s)/(0.14 m) = 14.3 rad/s
Ash
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