A particle of mass m moves in a circular path of radius r, under the action of force which deliver it a constant power p and increases its speed. the angular acceleration of particle at time t is proportional

Here, the only work done is in the direction of motion which causes acceleration.Power, p=Force×Speed in direction of force=Mass×acceleration×speed=m×dvdt×vwhere,dvdt=Linear acceleration.vdvdt=pm[ p is constant]Integrating,12v2=(pm)×t12()2=(pm)×tor ω2=2pmr2×tor w=2pmr2×t=ct1/2where, c=constantThus, the angular acceleration isdt=12ct-1/2i.e. angular acceleration is proportional to t-1/2 or 1t

  • 122
What are you looking for?