velocity / acceleration?

Question

a ferris wheel rotates at an angular velocity of 0.24 rad/s. starting from rest, it reaches its operating speed with an average angular acceleration of 0.030 rad/s^2. how long does it take the wheel to come up to operating speed and how do you mathmatically write this out?

Answer 1

It takes 8 seconds to "come up to speed." Here's how you show this, with EVERY step included:

After t seconds starting from rest, with an angular acceleration of 0.030 rad/sec^2, the angular speed will be 0.030 t rad/sec^1. So, you need to solve the equation:

0.030 t = 0.240, that is t = 0.240/0.030 = 8 seconds.

So, after 8 seconds, the angular speed will be 0.240 rad/sec^1.

QED

Live long and prosper.

Answer 2

Let me give you the same problem, but in muffins.

If I make 3 muffins a second (I'm very fast) and I need to make 24 muffins, how long do I need to make muffins for?

You are gaining 0.030 radians/s of angular speed every second and need to know how long it take to get up to 0.24 radians/s of speed.

It's essentially the same problem.

Answer 3

Initial Velocity u rad/sec

acceleration a rad/secxsec

final velocity v rad/sec. time duration of motion

v = u +at
.24 = .o30 x t

t = 8 sec