A disk turns through an angle of β(t)=Ct2 - Bt3 where C=3.20 rad/s2 and B= 0.500...

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 velocity w(t) as a function of time.

Solutions

Expert Solution

C = 3.2 rad/s²

B = 0.5 rad/s³

Angle through which the disk turns is given by,

(t) = Ct² - Bt³

(t) = 3.2t² - 0.5t³

Angular velocity is the rate of change of angle with respect to time.

If we differentiate the equation of the angular position of the disk with respect to time we will get the angular velocity of the disk.

(t) = 6.4t - 1.5t²

Angular acceleration is the rate of change of angular velocity with respect to time.

If we differentiate the equation of the angular velocity of the disk with respect to time we will get the angular acceleration of the disk.

(t) = 6.4 - 3t

a) Angular acceleration as a function of time is given by,

(t) = 6.4 - 3t

b) Angular velocity as a function of time is given by,

(t) = 6.4t - 1.5t²

genius_generous answered 3 weeks ago

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