Revolutions of a tire and angle in radians thru warranty

[chaotiiic]

Homework Statement

The tires on a new car have a radius of .275 meters and are warranted for 75,000km

a)what is the angle in radians that one of these tires will rotate thru in the warranty period?
b) how many revolutions does this make?

Homework Equations

1rev = 2pi radians
circumference = 2pi*r

The Attempt at a Solution

circumference = (2pi)(.275m) = 1.727m
b) 75m/.001727= 43427.9
a) 43427 *2pi = 272865

 

[Pengwuino]

Your calculation for b) is wrong. You should find the number of revolutions as ${{75,000,000m}\over{1.727 {{m}\over{turn}}}}$

 

[chaotiiic]

Your calculation for b) is wrong. You should find the number of revolutions as ${{75,000,000m}\over{1.727 {{m}\over{turn}}}}$

43,427,909.66 revolutions.
to find the angle do i multiply this by 2pi?

 

[Pengwuino]

43,427,909.66 revolutions.
to find the angle do i multiply this by 2pi?

Yes.

 

[asteriatic]

.3 radiansI would like to clarify a few things about this problem.

Firstly, the statement "revolutions of a tire and angle in radians" is not entirely clear. It would be more accurate to say "rotations of a tire and the angular displacement in radians." This is because revolutions refer to a complete circular motion, while rotations refer to any partial circular motion.

Secondly, the use of "warranty" in this context is also not entirely clear. It is assumed that the warranty refers to the expected lifespan of the tires, but it would be helpful to specify what type of warranty this is (e.g. manufacturer's warranty, extended warranty, etc.).

With that being said, let's proceed with the solution:

a) The tire's radius is 0.275 meters, which means its circumference is 2π(0.275) = 1.727 meters. In 75,000 km, the tire would have traveled 75,000,000 meters. Dividing this by the circumference gives us the number of rotations: 75,000,000/1.727 = 43,427.9 rotations.

To convert this to radians, we multiply by 2π, giving us a total angular displacement of 272,865.3 radians.

b) As mentioned before, the tire would have rotated 43,427.9 times in 75,000 km. This is equivalent to 43,427.9 revolutions.