# Angular Acceleration, Max/Min, and Grav. Attraction

• the7joker7
In summary, the three questions on my physics homework are: 1) What is the angular acceleration of a tire placed on a balancing machine? 4.7 = .5(a)(1.2^{2}) and it is 40.98 radians/second. 2) A car can round a curve where the radius of curvature of the road is R, the banking angle is theta, and the coefficient of static friction is mu. Find the range of speeds the car can have without slipping up or down the road, and what is the range of speeds possible if R = 100m, theta = 10 degrees, and mu = 0.10? The car can have a speed range of 8.
the7joker7
Here are three questions on my physics homework and my attempts to solve them...am I looking at this the right way?

Question 1: A tire placed on a balancing machine in a service station starts from rest and turns through 4.7 revolutions in 1.2 seconds before reaching it's final angular speed. Calculate its angular acceleration.

My attempt: Using formula x(t) = x$$_{0}$$+ v$$_{0}$$*T + (.5)at$$^{2}$$

I got

4.7 = .5(a)(1.2$$^{2}$$)

Solving for a, I got 6.522 rotations, or 40.98 radians.

Question 2: A car rounds a banked curve where the radius of curvature of the road is R, the banking angle is theta, and the coefficient of static friction is mu. Find the range of speeds the car can have without slipping up or down the road, and what is the range of speeds possible if R = 100m, theta = 10 degrees, and mu = 0.10?

The formula I pounded out was...

$$\sqrt{(((r*g(sin(\theta) - \mu(cos(\theta))))/(cos(\theta) + \mu(sin(\theta))}$$ < V < $$\sqrt{((r*g(sin(\theta) + \mu(cos(\theta))))/(cos(\theta) - \mu(sin(\theta)))}$$

I plugged in the numbers and wound up with 8.57 < V < 16.603, in any case, which I'm sure is right so long as my formula is right.

Question Three: Two schoolmate, Romeo and Juliet, catch each other's eye across a crowded dance floor at a school dance. Find the order of magnitude of the gravitational attraction that Juliet exerts on Romeo and vice versa. State quanities you take as data and the values you measure or estimate for them.

I basically just guessed my own masses (Romeo is 80kg and Juliet is 70kg) and the distance between is 12m. I used the formula

((m$$_{1}$$*m$$_{2}$$)/distance$$^{2}$$)*gravity to get 381.11N, of magnitude 10^2~.

That work?

Last edited:
Please post in the HW help section, and please revise you post using the text tool bar. I can't read what you wrote.

Its the equation editor in advanced mode.

I'm not seeing the equation editor when I went to advanced mode...where is it?

There is a small sigma symbol up top on the tool bar.

Thanks! I've cleaned it up.

## 1. What is angular acceleration?

Angular acceleration is the rate of change of angular velocity, which is the change in rotational speed over time. It is measured in radians per second squared (rad/s²) and is a measure of how quickly an object is rotating.

## 2. How is angular acceleration different from linear acceleration?

Angular acceleration is the change in rotational speed, while linear acceleration is the change in linear speed. Angular acceleration is measured in radians per second squared, while linear acceleration is measured in meters per second squared.

## 3. How do you calculate the maximum and minimum values of angular acceleration?

To calculate the maximum and minimum values of angular acceleration, you need to know the initial and final angular velocities, as well as the time it takes for the change to occur. The maximum angular acceleration occurs when the final angular velocity is greater than the initial angular velocity, and the minimum angular acceleration occurs when the final angular velocity is less than the initial angular velocity.

## 4. What is the relationship between angular acceleration and gravitational attraction?

Angular acceleration and gravitational attraction are not directly related. Angular acceleration is a measure of rotational speed, while gravitational attraction is a force that acts between two objects with mass. However, angular acceleration can be affected by gravitational attraction if the object is in orbit or is rotating around a central point due to the gravitational force.

## 5. How can angular acceleration be applied in real life?

Angular acceleration is applied in many real-life situations, such as in the motion of planets and satellites, the rotation of wheels on a car, and the spinning of a top or a gyroscope. It is also important in understanding the stability and control of objects in motion, such as in sports like gymnastics and figure skating.

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