A gyroscope rotates through and angle of 200 radians while accelerating from rest at 2.5 rad/s2. a. How long does it take to reach 200 radians?
b. What is it final angular velocity?
c. What is the linear velocity at its edge (R = 0.05 m)?

Suppose that f : rn → rm and that a ∈ k, where k is a connected subset of rn . suppose further that for each x ∈ k there exists a δx > 0 such that f(x) = f(y) for all y ∈ bδx (x). prove that f is constant on k; that is, f(x) = f(a) for all x ∈ k