# Homework Help: Angular and linear velocity

1. Aug 12, 2011

### aghakarim

5. A roller 0.44 m diameter rolls down a slope starting from rest. It takes 12 seconds make 6 complete rotations along the sloping surface accelerating uniformly as it moves. Calculate the following:

(1). The angular velocity at the end.

(2). The linear velocity at the end.

(3). The angular acceleration.

(4). The linear acceleration.

(5). The distance travelled.

from the question its obvious each rotation takes two seconds

12/6=2
then i thought omega= (2*pi)/12 gives you rads per second
but i then got really confused as i actualy dont have the velocity in the question and i lost it all

is the angular velocity (number of revs*2*pu)/number of cycle?

any ideas? i am losttt!!!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Aug 12, 2011

### kuruman

Start from the kinematic equations for rotational motion. Although 12/6 is always equal to 2, this is irrelevant here. Each complete revolution takes less time as the roller accelerates down the incline. Furthermore, the angular velocity also changes as time increases.

3. Aug 12, 2011

### aghakarim

but wouldnt all reveloutions be the same since the rollers speed is the same and in move uniformly?

4. Aug 12, 2011

### aghakarim

also is this equation right to work out the final velocity?

v=2*pi*r/t

then the answer times the number of rotation?
or more needs to be done or is this wrong?

5. Aug 12, 2011

### kuruman

The roller's speed is not the same at all times. It starts from rest and this means that its initial velocity is zero. If the roller's velocity were the same at all times, its velocity would remain at zero and the roller would stay where it is, at the top of the incline. This is not what happens. The roller rolls down the incline which means that its velocity changes from zero to something other than zero. Therefore the roller accelerates and this means that its velocity is not the same at all times.
It is not right because it assumes that the acceleration is zero, i.e. that the roller makes the same number of revolutions in the same amount of time. As I just pointed out, the acceleration cannot be zero.

Like I said, what are the kinematic equations for rotational motion under constant acceleration? There are four of them. Write them down and see whether you can figure out which one to use considering what is given to you.