A roller in printing press, with a shape of a solid cylinder and has a mass of 5 kg, turns through an angle θ(t) given by θ(t) = γt^(2) – βt^(3), where γ = 3.20 rad/s^(2) and β = 0.500 rad/s^(3).
a. What is the maximum positive angular velocity and
b. at what value of t does it occur?

Question

A roller in printing press, with a shape of a solid cylinder and has a mass of 5 kg, turns through an angle θ(t) given by θ(t) = γt^(2) – βt^(3),  where γ = 3.20 rad/s^(2) and β = 0.500 rad/s^(3). 
    a. What is the maximum positive angular velocity and 
    b. at what value of t does it occur?

anonymous · Answer

is it correct?  a. angular velocity = 20.48 rad/s b. t = 6.4 s

irishboy123 · Answer

are you using calculus?!?!

because from $ θ(t) = γt^2 – βt^3$ , we have $\dot θ(t) = 2γt – 3βt^2$ and $\ddot θ(t) = 2γ – 6βt = 0 \implies t_{\dot \theta_{max}} = \dfrac{\gamma}{3 \beta} = 2.1\dot 3 \, s$ for max ang vel.  [$\dddot {\theta} <0 $ so it is a max]

have a look here at plot of ang velocity (v) and ang acceleration (a) to clarify....

i was wondering how you got a) before b) and suspect maybe you are plotting it ....or maybe i am just really missing the point :-))  lol

irishboy123 · Answer

this is the plot i referred to but failed to include:

|dw:1450173493296:dw|

irishboy123 · Answer

😋