Question

4. A cylinder with mass M = 2 kg rotates around its major axis (figure). Its angular position is given by this relation, θ = 2 ??? ? ?2 + 50 ??? ? + 39 ???. Calculate

(Hint: we must derive)

a) Angular velocity and direction

b) Angular acceleration and direction

c) Initial angular position

d) Calculate the net torque on the cylinder and the torque direction

e) Make a graph of angular velocity vs. Weather

f) Identify the initial velocity in the graph

g) How many revolutions (turns) the cylinder gives in 20s

Answer 1

a)

angular position is given as

= 2 t² + 50 t + 39

taking derivative both side relative to "t"

d/dt = d/dt (2 t² + 50 t + 39)

w = 4 t + 50 since w = d/dt

b)

angular velocity is given as

w = 4 t + 50  

taking derivative both side relative to "t"

dw/dt = (d/dt) (4 t + 50 )   

= 4 Since dw/dt =

c)

angular position is given as

= 2 t² + 50 t + 39

initially at t = 0

= 2 (0)² + 50 (0) + 39

= 39 rad

g)

number of revolutions is given as

N = /(6.28) = ( 2 t² + 50 t + 39)/6.28 = ( 2 (20)² + 50(20) + 39)/6.28 = 292