A bicycle wheel has an initial angular velocity of 1.10 rad/s . Part A If its angular acceleration is constant and equal to 0.200 rad/s2 , w

Question

A bicycle wheel has an initial angular velocity of 1.10 rad/s . Part A If its angular acceleration is constant and equal to 0.200 rad/s2 , what is its angular velocity at t = 2.50 s ? (Assume the acceleration and velocity have the same direction) Express your answer in radians per second. ω = nothing rads Request Answer Part B Through what angle has the wheel turned between t = 0 and t = 2.50 s ? Express your answer in radians. Δθ = nothing rad Request Answer Provide Feedback

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Kiệt Gia 3 years 2021-08-26T13:54:29+00:00 1 Answers 320 views 0

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  1. giabao
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    2021-08-26T13:55:37+00:00
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    Let \theta, \omega, and \alpha denote the angular displacement, velocity, and acceleration of the wheel, respectively.

    (A) The wheel has angular velocity at time t according to

    \omega=\omega_0+\alpha t

    so that after 2.50 s, the wheel will have attained an angular velocity of

    \omega=1.10\dfrac{\rm rad}{\rm s}+\left(0.200\dfrac{\rm rad}{\mathrm s^2}\right)(2.50\,\mathrm s)=\boxed{1.60\dfrac{\rm rad}{\rm s}}

    (B) The angular displacement of the wheel is given by

    \theta=\theta_0+\omega_0t+\dfrac\alpha2t^2\implies\Delta\theta=\omega_0t+\dfrac\alpha2t^2

    After 2.50 s, the wheel will have turned an angle \Delta\theta equal to

    \Delta\theta=\left(1.10\dfrac{\rm rad}{\rm s}\right)(2.50\,\mathrm s)+\dfrac12\left(0.200\dfrac{\rm ram}{\mathrm s^2}\right)(2.50\,\mathrm s)^2=\boxed{3.38\,\mathrm{rad}}

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