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27 May, 12:56

The angular position of objects as a function of time is given, where a, b, and care constants. In which of these cases is the angular acceleration constant? Select all correct answers (Hint: there is more than one.) Select one or more B. 0 - ar + b ii. O = ar?. btc ili. 8 - at? - iv. 0 = sin (at)

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  1. 27 May, 13:51
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    The options is not well presented

    This are the options

    A. θ = at³ + b

    B. θ = at² + bt + c

    C. θ = at² - b

    D. θ = Sin (at)

    So, we want to prove which of the following option have a constant angular acceleration I. e. does not depend on time

    Now,

    Angular acceleration can be determine using.

    α = d²θ / dt²

    α = θ'' (t)

    So, second deferential of each θ (t) will give the angular acceleration

    A. θ = at³ + b

    dθ/dt = 3at² + 0 = 3at²

    d²θ/dt² = 6at

    α = d²θ/dt² = 6at

    The angular acceleration here still depend on time

    B. θ = at² + bt + c

    dθ/dt = 2at + b + 0 = 2at + b

    d²θ/dt² = 2a + 0 = 2a

    α = d²θ/dt² = 2a

    Then, the angular acceleration here is constant is "a" is a constant and the angular acceleration is independent on time.

    C. θ = at² - b

    dθ/dt = 2at - 0 = 2at

    d²θ/dt² = 2a

    α = d²θ/dt² = 2a

    Same as above in B. The angular acceleration here is constant is "a" is a constant and the angular acceleration is independent on time.

    D. θ = Sin (at)

    dθ/dt = aCos (at)

    d²θ/dt² = - a²Sin (at) = - a²θ

    α = d²θ/dt² = - a²θ

    Since θ is not a constant, then, the angular acceleration is dependent on time and angular displacement

    So,

    The answer is B and C
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