# Circular motion with tangential acceleration

• vu10758
In summary, a car is traveling on a flat circular track with tangential acceleration a_tan and radius r. The coefficient of static friction mu is used to determine the total distance traveled before the car skids off the track. The free body diagram includes normal force, weight, and a force pointing towards the center of the circle. Using the equations N=mg and F=ma, as well as knowledge of d=(1/2)at^2 and v=SQRT(Fr/m), the distance can be calculated. However, the answer provided, d = mu*g*r/2a, is incorrect and instead, the force of static friction must provide the total acceleration for the correct answer.
vu10758
A car is initially at rest. It starts mvoing with tangential acceleration a_tan along a flat circular track of radius r. If the coefficient of static friction is mu, determine the total distance traveled by the car before it skids off the track.

This is what I did.

I drew the free body diagram with normal force point up, mg pointing down, and f point right, and acceleration (not on the diagram) is pointing left towards the center. Is this the correct diagram?

I know N=mg

and

F = ma
F = m (v^2)/r

so v=SQRT(Fr/m)

I know d = (1/2)at^2

Where do I go from here to find the distance. I don't have acceleration and time.

In your free body diagram, you are missing something that relates to the friction...

Just think about which is the force that keeps the car in circular motion.
(The answer is d = mu*g*r/2a.)

aster said:
Just think about which is the force that keeps the car in circular motion.
(The answer is d = mu*g*r/2a.)

In any case, that answer is incorrect. Hint: Static friction must provide the total acceleration.

## 1. What is circular motion with tangential acceleration?

Circular motion with tangential acceleration is a type of motion where an object moves in a circular path while also experiencing a change in its speed or velocity. This change in velocity is known as tangential acceleration.

## 2. What causes tangential acceleration in circular motion?

Tangential acceleration in circular motion is caused by a change in the object's speed or direction. This is typically due to a force acting on the object, such as gravity or a centripetal force.

## 3. How is tangential acceleration calculated?

Tangential acceleration can be calculated using the formula a = rα, where a is the tangential acceleration, r is the radius of the circular path, and α is the angular acceleration. It can also be calculated using the equation a = v²/r, where v is the linear speed of the object.

## 4. How is tangential acceleration different from centripetal acceleration?

Tangential acceleration and centripetal acceleration are both components of the overall acceleration in circular motion. Tangential acceleration is the change in speed, while centripetal acceleration is the change in direction. They are perpendicular to each other and together make up the total acceleration of an object in circular motion.

## 5. What are some real-life examples of circular motion with tangential acceleration?

Some real-life examples of circular motion with tangential acceleration include a car moving around a curved road, a rollercoaster moving along its track, and a satellite orbiting the Earth. The changing speed and direction of these objects result in tangential acceleration.

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