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Unformatted text preview: 6. If we make the units explicit, the function is θ = 2.0 rad + ( 4.0 rad/s 2 ) t 2 + ( 2.0 rad/s3 ) t 3
but in some places we will proceed as indicated in the problem—by letting these units be understood. (a) We evaluate the function θ at t = 0 to obtain θ0 = 2.0 rad. (b) The angular velocity as a function of time is given by Eq. 10-6: ω= dθ = ( 8.0 rad/s 2 ) t + ( 6.0 rad/s3 ) t 2 dt which we evaluate at t = 0 to obtain ω0 = 0. (c) For t = 4.0 s, the function found in the previous part is ω4 = (8.0)(4.0) + (6.0)(4.0)2 = 128 rad/s.
If we round this to two figures, we obtain ω4 ≈ 1.3 × 102 rad/s. (d) The angular acceleration as a function of time is given by Eq. 10-8: α= dω = 8.0 rad/s 2 + (12 rad/s3 ) t dt which yields α2 = 8.0 + (12)(2.0) = 32 rad/s2 at t = 2.0 s. (e) The angular acceleration, given by the function obtained in the previous part, depends on time; it is not constant. ...
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This note was uploaded on 05/17/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.
- Spring '08