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Two of the tires on a tractor-trailer have 1.5 m diameters. If the tractor-trailer travels at a linear velocity of 3.0 m/s, what is the angular velocity of each tire?

Answer 1

Leo Abeyta

I got #2"rad"/s#

I would use the relationship between linear velocity #v#, radius #r# and angular velocity #omega#:

#v=omegar#

Organizing:

#omega=v/r=3/1.5=2"rad"/s#

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Answer 2

Axel Acevedo

To find the angular velocity of each tire, we can use the formula:

[ \text{Angular velocity} = \frac{\text{Linear velocity}}{\text{Radius}} ]

Given that the diameter of each tire is 1.5 meters, the radius (r) is half of the diameter, so ( r = 0.75 ) meters.

Plugging in the values, we get:

[ \text{Angular velocity} = \frac{3.0 , \text{m/s}}{0.75 , \text{m}} = 4.0 , \text{rad/s} ]

Therefore, the angular velocity of each tire is ( 4.0 , \text{rad/s} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.