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Unformatted text preview: Physics 106, Spring 2008 K. Kauder Group Problem #4 –Answer key– 1. ♠ A wheel starts from rest with a constant angular acceleration of 2.6 rad s 2 and rolls for 6 s. At the end of that time, (a) what is its angular velocity? Solution : ω = α t = 15 . 6 rad s (b) Through what angle has the wheel turned? Solution : θ = 0 + 0 t + 1 2 α t 2 = 46 . 8 rad (c) How many revolutions has it made? Solution : θ 2 π = 7 . 448 The wheel makes 7 full rotations; the final angle θ ′ is given by the fractional part times 2 π . θ ′ = 0 . 448(2 π ) = 2 . 51 rad (d) What is the speed and acceleration of a point 0.3 m from the axis of rotation? Solution : v = r ω = 4 . 68 m s vectora = r α ˆy + r ω 2 ˆx = (0 . 78 m s 2 ) ˆy (73 . 00 m s 2 ) ˆx Centripetal and tangential acceleration point in perpendicular directions, here chosen to be ˆx and ˆy .  vectora  = radicalbig (0 . 78 m s 2 ) 2 + (73 . 00 m s 2 ) 2 = 73 . 004 m s 2 2. ♥ When a turntable rotating at 33 1 3 rpm is shut off, it comes to rest in 26 s. Assuming constant angularrpm is shut off, it comes to rest in 26 s....
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 Spring '08
 KOJA
 Physics, Acceleration, Rotation, Angular velocity, quito

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