The angle through which a rotating wheel has turned in time t is given by = a t
ID: 1612531 • Letter: T
Question
The angle through which a rotating wheel has turned in time t is given by = a t b t2+ c t4, where is in radians and t in seconds.
A)Determine an expression for the instantaneous angular velocity if t is in seconds.
= ______ rad/s
B)Determine an expression for the instantaneous angular acceleration if tis in seconds.
= _______ rad/s^2
c)If a = 9.0 rad/s , b = 14.5 rad/s2 , c = 1.5 rad/s4 , evaluate at t = 3.2 s .
= _____ rad/s
d)Evaluate at t = 3.2 s .
= ______ rad/s^2
e) What is the average angular velocity between t = 2.0 s and t =3.2 s ?
avg = _______ rad/s
f)What is the average angular acceleration between t = 2.0 s and t =3.2 s ?
avg = ____ rad/s^2
= _______ rad/s^2
c)If a = 9.0 rad/s , b = 14.5 rad/s2 , c = 1.5 rad/s4 , evaluate at t = 3.2 s .
= _____ rad/s
d)Evaluate at t = 3.2 s .
= ______ rad/s^2
e) What is the average angular velocity between t = 2.0 s and t =3.2 s ?
avg = _______ rad/s
f)What is the average angular acceleration between t = 2.0 s and t =3.2 s ?
avg = ____ rad/s^2
Explanation / Answer
theta = at - b t^2 + c t^4
A)We know that,
w = d(theta)/dt
w = d(at - b t^2 + c t^4)/dt
w = a - 2 b t + 4 c t^3
b)we know that,
alpha = d(w)/dt
alpha = d(a - 2 b t + 4 c t^3)/dt
alpha = -2 b + 12 c t^2
c) w = a - 2 b t + 4 c t^3
w = 9 - 2 x 14.5 x 3.2 + 4 x 1.5 x 3.2^3 = 112.81 rad/s
Hence, w = 112.81 rad/s
d)alpha = -2 b + 12 c t^2
alpha = -2 x 14.5 + 12 x 1.5 x 3.2^2 = 155.32
Hence, alpha = 155.32 rad/s
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