Question

A) what is the angular velocity as a function of time?

B) what is the initial tangential velocity in m/s?

C) what is the angular acceleration in rad/s^2?

D) at what time does the cylinder stop spinning?

E) through how many rotations does the cylinder turn before stopping?

3. A cylinder with a radius of 0.5 m spins with and angle as a function of time: a. What is the angular velocity as a function of time?

Answer 1

(A) theta(t) = 5t - 2t^2 Therefore Angular velocity, theta(t) = d/dt (5t - 2t^2) or, theta(t) = 5 - 4t (B) Tangential velocity = r theta, r = radius Therefore Initial tangential velocity is V_T(t = 0) = r theta(t = 0) or, V_T(t = 0) = 0.5 times (5 - 4 times 0) or, V_T(t = 0) = 2.5 ms^-1 (C) Angular acceleration is theta(t) = d/dt (theta(t)) or, theta(t) = -4 (D) Spinning stops when theta = 0 Therefore 5 - 4t = 0 material implication t = 5/4 s (E) Stopping time, t_s = 5/4 s Angular displacement from t = 0 to t = t_s is theta(t = t_s) - theta(t = 0) = theta(t = t_s) - 0 or, theta(t = t_s) = 5(5/4) - 2(5/4)^2 or, theta(t = t_s) = 25/8 radians Therefore, No. of rotations = (25/8)/2pi = (25/8)/(2 times 22/7) = 25/8 times 7/44 = 0.497 rotations.