Question

The angle theta through which a disk drive is given by theta(t) = a+ bt - ct^3, where a, b and c are constants, t is measured is seconds, and theta is in radians. when t = 0 s, theta = pi/4 rad and the angular velocity w = 2.00 rad/s. when t = 1.50s, the angular acceleration a = 1.25 rad/s^2.

A) Find a, b, and c, including their units.

B) What is the angular acceleration when theta = pi/4 rad?

c) what are theta and the angular velocity when the angular acceleration is 3.50 rad/s^2?

Answer 1

(t) = a + bt - c t³

at t = 0

(0) = /4

a + b(0) - c (0)³ = /4

hence a = /4 = 0.785 rad

angular velocity is given as

w(t) = d(t) /dt = b - 3 ct²

at t = 0

w(0) = 2

b - 3 c (0)² = 2

b = 2

angular acceleration is given as

(t) = dw(t)/dt = - 6ct

at t = 1.5

(1.5) = 1.25

- 6c (1.5) = 1.25

c = - 0.139

B)

when

(t) = /4

/4 + (2)t - (-0.139) t³ = /4

t = 0

at t = 0

(t) = 0

c)

(t) = 3.50

- 6ct = 3.50

- 6 (-0.139) t = 3.50

t = 4.2 sec

(t) = a + bt - c t³

(4.2) = (0.785) + (2) (4.2) - (-0.139) (4.2)³

(4.2) = 19.5 rad