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Chapter11

# Chapter11 - 1 The velocity of the car is a constant ^ v =...

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2. The initial speed of the car is ( ) 80 km/h (1000 m/km)(1 h/3600 s) 22.2 m/s v = = . The tire radius is R = 0.750/2 = 0.375 m. (a) The initial speed of the car is the initial speed of the center of mass of the tire, so Eq. 11-2 leads to com0 0 22.2 m/s 59.3 rad/s. 0.375 m v R ω = = = (b) With θ = (30.0)(2 π ) = 188 rad and ω = 0, Eq. 10-14 leads to ( ) 2 2 2 2 0 (59.3 rad/s) 2 9.31 rad/s . 2 188 rad ω ω αθ α = + ¡ = = (c) Eq. 11-1 gives R θ = 70.7 m for the distance traveled.
For a uniform disk (relative to its center of mass) I mR = 1 2 2 (Table 10-2(c)). Since the wheels roll without sliding ω = v / R (Eq. 11-2). Thus the numerator of our fraction is 4 4 1 2 2 2 2 2 2 I mR v R mv ω = F H G I K J F H G I K J = and the fraction itself becomes ( ) 2 2 2 2 10 2 2 1 fraction 0.020.

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