Hey,
I dont understand if we are supposed to take the omega_2 as zero or not.
As its minimum speed required doesnt that mean that v_2 should be zero. So if v_2 is zero then i thought omega _2 should be zero as velocity of center of mass depends on the angular velocity when it hits the curb.
1 comment:
There are three instants in time that are of interest for this problem:
1 - immediately before vehicle strikes curb,
2 - immediately after vehicle strikes curb, and
3 - when the CM of the vehicle is directly above the curb.
You can NOT use either conservation of angular momentum or conservation of energy throughout the ENTIRE process since energy is not conserved during impact and angular momentum is not conserved after impact.
* During 1-2: Here angular momentum about the curb is conserved. For 1, v1 is as given and omega1 = 0 (since vehicle is in pure translation). omega 2 is found from the conservation of angular momentum equation. From this you find v2 = d*omega2, where d is the distance from the CM to the curb (since vehicle is rotating about the curb).
* During 2-3: Here energy is conserved. You know v2 and omega2 from above. Since you are wanting to know the minimum v1 to cause rollover you will use v3 = 0 and omega3 = v3/d = 0.
Let us know if this does not help.
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