Let's find the linear velocity of a point on the rim of this shaft flange. To calculate the linear velocity wee need to know how far the point is traveling in a second. as it is traveling in a circle, we need the circumference of the circle on which it is traveling:

Now we can convert the 1000 RPM given in the question to see how many revolutions we have a second:

If we travel 0.62832m every revolution, and we do 16.6666 revolutions every second, by multiplying these two values we can find how far a point on the rim will travel every second:

In order to calculate the acceleration, we are going to use a SUVAT. This is angular acceleration, and there is an angular set of SUVAT equations, but as they are essentially the same as the linear ones, and to save us having to learn more formulas than needed, let's just use regular SUVAT.

First, we will need to convert the units in the question into the Units required in the answer. We need the acceleration to be in Rads/sec ^2, so let's convert the initial velocity and the final velocities from RPM to Rads per second:

We turn Revs to rads by multiplying by 2pi, and then 1 minute into one second by dividing by 60. (again there are shortcuts for this, but as we spend ALOT of time converting units, I find this method is easier to remember, understand, and check).

Now we can solve that SUVAT:

we calculated this in the previous section!

To calculate the linear velocity we need to find the distance traveled every second by a point on the rim. We will be using the simple formula for speed (its basically the same as velocity, and will make it easier to remember). So we need the distance traveled every second.

The distance traveled by a point on the rim will be the circumference of the circular path traveled, so we need the circumference, which we just calculated above. This is the distance traveled in one rotation.

Next, we need to see how many rotations the flywheel is doing per min, the question is a little harder as they gave us rads per min, so let's convert into revolutions (rotations)

In order to get the distance traveled, we multiply the circumference by the number of revolutions, and we can write this over 1 min as a fraction as we were given the number of rads per min.

the last step here is to convert the distance traveled in 60 seconds down to 1 second, giving us 67.29 m/s as the answer.

Converting units is a big part of this test, first, let's convert RPM to rads per second for both the starting and the final velocities

First, we divide RPM by 60 to get revolutions per second

Then we can multiply by 2pi to convert from Revolutions to Radians. (For example, if we had 1 rev this would be 2pi rads)

We do this for both the initial and final velocities

Now we can find the acceleration in rads per second^2 using a SUVAT

We need to convert from degrees to radians. This is very common in this section of the test, to be able to convert between radians, degrees and revolutions. We will make a table, starting with a fact we know: 360º= 2pi radians.

Then we will convert 360 into the required 150. Todo this we will divide 360 by 360 to get 1, then multiply by 150 to get 150 (just like we do with percentages!) anything we do to one side, we will also to do the other, this will maintain the proportional relationship. Again we have to ALOT of conversions as an engineer, so building this table allows for easy conversion of units.

A large part of this test, and the skills you require is converting units. Here we will spend some time converting between; Revolutions, Degrees and Radians.

First, we can write this out as a fraction. Then we can convert Radians into Degrees. Next 1 minute into 60 seconds. Finally, we can simplify to get the number of degrees per second.

We can think of linear velocity in the same way as speed.

So we need to know the distance traveled and the time taken to cover that distance. The distance travelled by a point on the perimeter would be the circumference of the circle.

Let's explain the diagram above. we are given the velocity as 1000 revolutions per minute. The distance travelled in one revolution is the same as the circumference of the circle, this is given by Pi*D (pi*0.3) and we know that there are 60 seconds in a minute, so let's write it like that. Velocity is usually given in meters per (one) second, not sixty, so let's fix that by dividing it down: