P221_2008_week9 - Basic ideas(for sheet Work = F.d W = K...

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Basic ideas (for sheet) Work = F . d W = K Power = dW/dt (= F.v ) Kinetic Energy: K = ½ mv 2 P.E. U g = mgh U el = ½ k(x-x o ) 2 F = -dU/dx (e.g. Spring: F = -k(x-x o ) Mech. Eng. conserved if only conservative forces do work. Dissipative forces convert some Mech. Eng. to thermal energy. Center of Mass R = Σ (m i r i )/ Σ m i P = m v F = d P /dt => momentum is conserved if there are no outside forces Rocket formula: (dM/dt)V=Ma v-v o =-Vln(M o /M) Defns: Elastic, Perfectly inelastic, etc. for collisions, Conservative forces
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A car accelerates at a constant rate of 2.60 m/s2 along a straight line. Assuming that its tires roll without slipping on the road, and that they have a diameter of 45.0 cm, what is the angular acceleration of each tire? If the car started from rest, what would be the angular velocity of the tires after 4.0 seconds of acceleration? (8 knew how to answer this [but only 4 got it right]; 13 made various errors [mainly not distinguishing v and ϖ ] 23 no answer).
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