Reading through the questions, we come across angular acceleration and distance covered. We, therefore, know that this is a rotational kinematics problem.

Rotational kinematic equations:

$\overline{){{\mathbf{\omega}}}_{{\mathbf{f}}}{\mathbf{=}}{{\mathbf{\omega}}}_{{\mathbf{0}}}{\mathbf{}}{\mathbf{+}}{\mathbf{}}{\mathbf{\alpha}}{\mathbf{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathbf{\theta}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{(}}{{\mathbf{\omega}}}_{{\mathbf{0}}}{\mathbf{+}}{{\mathbf{\omega}}}_{{\mathbf{f}}}{\mathbf{)}}{\mathbf{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathbf{\theta}}{\mathbf{=}}{{\mathbf{\omega}}}_{{\mathbf{0}}}{\mathbf{t}}{\mathbf{}}{\mathbf{+}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{\alpha}}{{\mathbf{t}}}^{{\mathbf{2}}}\phantom{\rule{0ex}{0ex}}{{\mathbf{\omega}}}_{{\mathbf{f}}}^{{\mathbf{2}}}{\mathbf{=}}{{\mathbf{\omega}}}_{{\mathbf{0}}}^{{\mathbf{2}}}{\mathbf{+}}{\mathbf{2}}{\mathbf{\alpha}}{\mathbf{\u2206}}{\mathbf{\theta}}}$

Δθ is the angle of rotation. The angle of rotation is not given, but we can determine it from the number of revolutions.

The tires of a car make 77 revolutions as the car reduces its speed uniformly from 92.0 km/h to 60.0 km/h. The tires have a diameter of 0.84 m.

1. What was the angular acceleration of the tires?

2. If the car continues to decelerate at this rate, how much more time is required for it to stop?

3. If the car continues to decelerate at this rate, how far does it go? Find the total distance.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Equations of Rotational Motion concept. You can view video lessons to learn Equations of Rotational Motion. Or if you need more Equations of Rotational Motion practice, you can also practice Equations of Rotational Motion practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Uppu's class at IOWA.