The angular position of a point on the rim of a rotating wheel is described by p

Question

The angular position of a point on the rim of a rotating wheel is described by phi= 4t -3t^2 +t^3 a) What is the average angular velocity at t_1 = 2s and t_2 = 4s? b) What is the instantaneous angular velocity at t = 3s? c) Find the expression for the angular acceleration. Is it a constant? If not, then, when is the acceleration equal to zero? A small block changes height from h = 5R to h = 0 (at B). Take + direction downward. m = 0.5 kg, R = 0.25 m a) Find the work done by gravity from point A to B. b) The block was able to reach point C. What is the work done by gravity? c) Use conservation of energy to find the velocity at point C.

Explanation / Answer

a)
Angular velocity at t=2 s
w = d/dt(4t-3t^2+t^3) = 4-6t+3t^2
=> w2 = 4 rad/s
and
=> w4 = 28 rad/s

b)
w3 = 4-6t+3t^2
= 4-6(3)+3(3)^2 = 13 rad/s

c) a = dw/dt
= d/dt(4-6t+3t^2)
= -6+6t

At t =1, a will be 0

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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