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A disk turns through an angle of β(t)=Ct2 – Bt3 where C=3.20 rad/s2 and B= 0.500 rad/s3. Calculate the angular acceleration α(t) and velocit
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Answers ( )
Answer:
ω(t) = 6.4 t – 1.5 t²
α(t) = 6.4 – 3 t
Explanation:
The angular displacement of the disk is given as the function of time:
β(t)=Ct² – B t³
where,
C = 3.2 rad/s²
B = 0.5 rad/s³
Therefore,
β(t) = 3.2 t² – 0.5 t³
Now, for angular velocity ω(t), we must take derivative of angular displacement with respect to t:
ω(t) = dβ/dt = (d/dt)(3.2 t² – 0.5 t³)
ω(t) = 6.4 t – 1.5 t²
Now, for angular acceleration α(t), we must take derivative of angular velocity with respect to t:
α(t) = dω/dt = (d/dt)(6.4 t – 1.5 t²)
α(t) = 6.4 – 3 t