00:01
For this problem, we are asked to get the difference between what happens if i assume that my radius stays the same, even though it does not.
00:10
What would happen to my linear velocity and my angular speeds? i should know these following equations either from your book or by memorizing them if you are not given them in the formula sheet, where my angular speed is equal to my distance, so my angle divided by my time, my linear speed is equal to my arc length divided by my time, and my arc length is equal to my radius times my angle.
00:40
And the angles are in radiance.
00:43
Now, if we assume that an angle is given here and it's one radiant, then we know that if i multiply s is r times theta, so i have this arc length is equal to one radius, which means i can now use this formula where my linear speed equals to my angular speed times my radius.
01:07
Then they say we are given a wheel.
01:10
The diameter in the middle of the wheel is 14 .5 inches, which means the radius is 7 .25 inches plus on either side or the tire side.
01:25
Side the rubber part is 4 .5 inches.
01:29
So i could say 7 .25 plus 4 .5 equals 11 .75 inches.
01:34
Or i can say to find the diameter, i would have to add both sides of the wheel or the rubber part on either side, so on the left hand side and the right hand side, and then the metal part in the middle.
01:46
So 4 .5 plus 14 .5 plus 4 .5, and if i divided by 2, i get the radius.
01:53
I am being told the cars traveling at 45 miles per hour and that i'm using the correct inches for my tires, which means i need to convert.
02:05
The one is using miles per hour, the other one is using inches.
02:09
And i want to know what is the rotations per second.
02:15
Then i'm going to say that to convert from miles per hour to inches per second, i have to multiply by the 45 by 5 ,000 to 180.
02:25
Times 12 in order to get from miles to inches.
02:30
Then i need to divide by 60 times 60 to get from hours to seconds.
02:37
So my final answer would be 792 inches per second.
02:43
To get the angular speed, i'm now going to say, what is my linear speed? so this equation over here.
02:50
So what is my linear speed, which was 792 inches per second, divided by my radius, which is 11 .75 inches.
03:00
I then get 67 .404 radiance per second.
03:04
The last step to find out how many rotations i have per second, i know if i divide this 67 .404 by 2 pi.
03:15
In other words, one full rotation is 2 pi.
03:19
I get one rotation.
03:21
So 67 .404 divided by 2 pi.
03:26
Is equal to 10 .728 rotations or revolutions per second.
03:38
So that's how many times my wheel will rotate per second...