Chapter_10_Problems

Chapter_10_Problems - Problem 10-4 The angular position of...

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Problem 10-4 θ = 4.0t – 3.0t 2 + t 3 a) At t = 2.0 ω = 4.0 rad/s b) At t = 4.0s ω = 28 rad/s e) α = 18 rad/s 2 The angular position of a point on the rim of a rotating wheel is given by θ = 4.0 t – 3.0 t 2 + t 3 , where θ is in radians and t is in seconds. What are the angular velocities at (a) t = 2.0 s and (b) t = 4.0 s? (c) What is the average angular acceleration for the time interval that begins at t = 2.0 s and ends at t = 4.0 s? What are the instantaneous angular accelerations at (d) the beginning and (e) the end of this time interval? ω = dθ/dt =4.0 – 6.0t + 3.0t 2 α = dω/dt = -6.0 + 6.0t c) α av = ∆ω/∆t = (24 rad/s)/2.0 s α av = 12 rad/s 2 d) α = 6.0 rad/s 2 ω = 4.0 – 6.0(2.0) + 3.0(2.0) 2 ω = 4.0 – 6.0(4.0) + 3.0(4.0) 2 α = -6.0 + 6.0(2.0) At t = 2.0 At t = 4.0s α = -6.0 + 6.0(4.0)
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In the time it takes the light to travel 2L, the wheel turns through an angle of ∆θ = 2π/500 ∆θ = 1.26 x 10 -2 rad The time required to travel 2L is ∆t = 2L/c
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Chapter_10_Problems - Problem 10-4 The angular position of...

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