Calculating Velocity

if you are a middle school student. you have to make clear what velocity are youi going to calculate?

angle velocity?

linear velocity is same. now you can get answer!

Sounds like they are saying a truck has wheels for example of 30" in diameter and if one wheel where changed to a 26" diameter then the smaller one would have a different velocity or RPM than the others.(rotating faster)

The rotational (angular) velocity of a wheel, for a given road speed, will vary inversely with its diameter. So, for example, a 36 in wheel will rotate 2/3 as fast as a 24" wheel, for the same road speed.

If you press the accelerater of the vehicle to the same extent in a particular gear then the vehicle with larger wheels will move faster.

Linear Velocity = Angular Velocity x Radius of wheel

Angular velocity = 2 x pi x n / 60 where n = rpm

The angular velocity can be assumed to be the same for a particular position of accelerator and gear (except for the slight increase in wt due to bigger wheels) all other conditions remaining the same.

Therefore if you incease the radius the linear velocity will increase.

The angular velocity can be assumed to be the same for a particular position of accelerator and gear

For wheels with different sizes,

A. Linear velocity of both wheels with different sizes (linear velocity is the speed of outer point at wheel OD contacted to the earth) are the same and equal to the linear velocity of truck.

B. Where the angular velocity of both wheels are differs :

e.g. for a fixed linear distance, each wheel must cuts the same distance (∏D . RPM),

so, ∏D1 . RPM1 = ∏D2 . RPM2, where RPM = Revolution Per Minute

D1 ⁄ D2 = RPM2⁄ RPM1

The angular velocity can be assumed to be the same for a particular position of accelerator and gear (except for the slight increase in wt due to bigger wheels) all other conditions remaining the same.

This is not technically true. The angular velocity can be assumed to be the same for a particular engine rpm, but not a particular throttle position. A truck driving up a hill of constant slope, will slow down, and the driver will apply increasing amounts of accelerator. If the hill is steep enough, eventually, the accelerator will be floored, and the truck will still slow, so the driver downshifts to increase tractive force. He may go through this cycle several times, and if he is in a hurry, the gear he settles in will permit the engine to run at it's maximum HP rpm, with all the horsepower consumed in rolling friction, aerodynamic drag, and climbing the grade. In any case, the accelerator can be wide open and the truck can be decelerating, (and going down hill, the throttle can be nearly closed and the truck can be going fast and accelerating). So there is no direct connection between throttle position and road speed or wheel rotational speed.

To prove that throttle position has little to do with speed, drive a manual transmission car of modest performance in fifth gear, at 50 mph. Floor the throttle. Speed changes very little and very slowly. Release the throttle completely. Again speed changes very little and very slowly. So in top gear, full throttle can equate to 50 mph, and zero throttle can equate to 50 mph.

Linear Velocity = Angular Velocity x Radius of wheel

In automotive engineering, angular velocity is expressed in RPM, (because we are not concerned with small portions of a revolution in drivetrains), with 1 r = 2 pi radians. (Many would then call this rotational velocity.) So this formula needs the addition of a 2 and a pi, to be easily understood in automotive terms. So, for example, 1000 wheel rpm, with a 1' wheel radius yields 1000 x 2 x pi fpm, or about 6280 fpm.

Therefore if you incease the radius the linear velocity will increase.

Increasing tire radius will increase linear velocity for a particular engine rpm and gear, but, in practice, the inverse occurs: speed remains the same, engine rpm goes down. (In fact, in practice, changing wheel size will not change road speed at all -- the driver still drives at the speed limit or slightly over.) In a vehicle with a top speed of 120, putting larger radius tires may decrease the top speed, because the engine rpm will drop, and the engine produces less HP at the lower engine speed. Many cars are "overgeared" with the top gear being designed for fuel economy and quiet running, but not for optimal top speed. Often, dropping down one gear gets the engine to its HP peak at top speed. (This assumes top speed is not electronically limited.)

When large wheel no.1 with dia. D1 rotates 1 cycle, it will cuts a linear distance ∏D1. For small wheel no.2 with dia. D2, must cuts the same linear distance (because both linear speeds of both wheels are the same = truck speed), so the small wheel must rotates a linear distance n.∏D2, where n is the no. of rotated cycles of wheel no.2 per 1 cycle of wheel no.1 & ∏ = 22⁄7.

∏.D1 = n.∏.D2

n = D1 ⁄ D2 , and Angular velocity ω2 = n.ω1

These pictures may help when considering relative wheel speed.

Great picture!!