The hoop will rolls vg = 2.75m/s for t = 1.32s before it stops slipping.
Solution:
mv1 = ∑∫F * dt = mv2
5(3) + 49.05 sin 30° (t) - 25.487 t = 5v(g)
(HG)1 + ∑∫ MGdt = (HG)2
-5(0.5)^2 * (8) + 25.487 (0.5) (r) = 5 (0.5)^ 2(vg)
Solving.
VG = 2.75 m/s
t = 1.32s
The object slides over the surface if the object's center of rotation moves faster than the velocity of rotation (vr). Such motion is referred to as sliding. Friction causes items in slipping motion to rapidly slow down to standstill, where they roll without slipping.
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