Converting Between Linear & Rotational Video Lessons

Concept

# 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:

$\overline{){{\mathbf{a}}}_{{\mathbf{t}}}{\mathbf{=}}{\mathbf{r}}{\mathbf{\alpha }}{\mathbf{=}}{\mathbf{r}}\frac{\mathbf{∆}\mathbf{\omega }}{\mathbf{∆}\mathbf{t}}}$

We'll use the equation of motion:

$\overline{){{{\mathbf{\omega }}}_{{\mathbf{f}}}}^{{\mathbf{2}}}{\mathbf{-}}{{{\mathbf{\omega }}}_{{\mathbf{0}}}}^{{\mathbf{2}}}{\mathbf{=}}{\mathbf{2}}{\mathbf{\alpha }}{\mathbf{\theta }}}$

We'll also use the motion equation:

$\overline{){{\mathbf{\omega }}}_{{\mathbf{f}}}{\mathbf{=}}{{\mathbf{\omega }}}_{{\mathbf{0}}}{\mathbf{+}}{\mathbf{\alpha }}{\mathbf{t}}}$

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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?