The angle ? theta through which a disk drive turns is given by ?(t)=a+bt?ct3 the

Question

The angle ? theta through which a disk drive turns is given by ?(t)=a+bt?ct3 theta(t) = abt - ct^3 , where aa ,bb and cc are constants, tt is in seconds, and ?theta is in radians. When t=0,?=?/4rad t = 0, theta = pi/4 rad and the angular velocity is 2.50rad/s rad/s , and when 1.60s s , the angular acceleration is 1.35rad/s2 rad/s^2 . a) What is the angular acceleration when ?=?/4rad theta =pi/4 rad ? b) What is ? theta when the angular acceleration is 4.00rad/s2 rad/s^2 ? c) What is the angular velocity when the angular acceleration is 4.00rad/s2 rad/s^2 ?

Explanation / Answer

?(t) = a + bt ?ct^3

at t = 0 ?(t) = pi/4

so , pi/4 = a = 0.785 rad

? = d?/dt = b - 3ct^2

at t= 0 ? = 2.5 rad/s

2.5 = b

? = d?/dt = -6ct

at t= 1.6 ....? = 1.35 rad/s^2

1.35 = -c*6*1.6

c = -0.140625

a = 0.785 rad ........b = 2.5 rad/s....c = -0.140625 rad/s^2

a) at ? = pi/4 .....t = 0

? = 0

b) ? = 4

? = 4 = -6ct

t = 4.74 s

?(t)=a+bt?ct^3 = (0.785)+(2.5*4.74)+(0.140625*4.74*4.74*4.74) = 27.61 rad

c) ? = b - 3ct^2 = (2.54)+(0.140625*4.74*4.74) = 5.67 rad/s

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.