# Relation between Angular speeds/accelerations

1. Sep 9, 2007

### mircobot

I have been having trouble with the following question on my homework:

wheel A of radius rA = 15 cm is coupled by belt B to wheel C of radius rC = 22 cm. The angular speed of wheel A is increased from rest at a constant rate of 1.6 rad/s2. Find the time needed for wheel C to reach an angular speed of 140 rev/min, assuming the belt does not slip.

HINT: The constant angular-acceleration equations apply. The linear speeds at the rims are equal. What then is the relation between the angular speeds and the angular accelerations?

2. Sep 9, 2007

### Staff: Mentor

For reference:

http://hyperphysics.phy-astr.gsu.edu/hbase/rotq.html
http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html

Now there are two concepts here.

1. A disc starts from rest at constant angular acceleration.

So find the equation that gives the angular velocity at the surface of A, at constant angular acceleration at time = t.

2. Then determine the tangential velocity of the belt B, v(t).

The belt drives disc C, so one has to convert v(t) to the angular velocity of C and when it reaches 140 rpm (pay attention to units; angular velocity is in rad/s). It's somewhat the reverse process of part 1.

3. Sep 9, 2007

### mircobot

the only equation i can think of that relates to a constant acceleration is v1 = v2 +at

i need some more help because i know that isn't right...

i found the time to be .4375s

4. Sep 10, 2007

### Staff: Mentor

One needs the analog of v1 = v2 +at for rotational motion.

$$\omega(t) = \omega_0 + \alpha*t$$, where $\omega(t)$ is angular velocity, and $\alpha$ is angular acceleration.

The linear or tangential velocity at radius r is just v(t) = $\omega(t)$*r,

and dividing by r, $\omega(t)$ = (v(t)/r.

5. Sep 10, 2007

### mircobot

alright, that helped a lot. now i see the relationship and substitution... also i was using A's radius, not C's.