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A wheel is rolling along a straight path without slipping. Determine velocity of points A, B and P. OP=600mm,ω=4rad/sec,V0=4m/s
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written 8.2 years ago by |
VA=?,VB=?OP=600mm,VP=?
ω=4rad/s,V0=4m/s
Instantaneous centre of wheel is at point of contact.
V0=I0.w∴I0=V0w=44=1m=1000mm
ID = Radius = 1000mm
IA = D = 2000 mm
And IB=√10002+10002=1414.2mmVA=IA.ω=2000×4=8000mm/s=8m/sVB=IB.ω=1414.2×4=5656.8mm/s=5.6568m/s∠POI=90+20=1100
By cosine rule,
IP=√(OP2+OI2−2.OP.OI.cos∠POIIP=√6002+10002−2×600×1000cos1100=1400mVP=IP.W=1400×4=5600m/s=5.6m/s
Instantaneous velocity of A=8m/s
Instantaneous velocity of B=5.6568m/s
Instantaneous velocity of C=5.6m/s