In: Physics
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.
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