Converting Between Linear & Rotational Video Lessons

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Problem: During a very quick stop, a car decelerates at 7.8 m/s2. Assume the forward motion of the car corresponds to a positive direction for the rotation of the tires (and that they do not slip on the pavement). Randomized Variables at = 7.8 m/s2 r = 0.26 m ω0 = 95 rad/s (a) What is the angular acceleration of its tires in rad/s2, assuming they have a radius of 0.26 m and do not slip on the pavement? (b) How many revolutions do the tires make before coming to rest, given their initial angular velocity is 95 rad/s ? (c) How long does the car take to stop completely in seconds?

FREE Expert Solution

Tangential acceleration:

at=rα=rωt

We'll use the equation of motion:

ωf2-ω02=2αθ

We'll also use the motion equation:

ωf=ω0+αt

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Problem Details

During a very quick stop, a car decelerates at 7.8 m/s2. Assume the forward motion of the car corresponds to a positive direction for the rotation of the tires (and that they do not slip on the pavement). 

Randomized Variables at = 7.8 m/s2 r = 0.26 m ω0 = 95 rad/s 

(a) What is the angular acceleration of its tires in rad/s2, assuming they have a radius of 0.26 m and do not slip on the pavement? 

(b) How many revolutions do the tires make before coming to rest, given their initial angular velocity is 95 rad/s ? 

(c) How long does the car take to stop completely in seconds?

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