Quick sign question for uniform circular motion

• hachi_roku
In summary, when calculating the maximum speed of a 1500kg car making a left turn on a level road, the equation f = mv^2/r should be used with the friction force being positive because it is in the direction of the turning center. The radial component is always positive when pointing towards the center in uniform circular motion problems.
hachi_roku

Homework Statement

what is the maximum speed with which a 1500kg car can make a left turn around a curve of radius 50m on a level road without sliding?

The Attempt at a Solution

f_s points left and the equation sigmaF_r =
f_s = mv^2/r

why isn't it negative if the force in the free body is pointing left? is it because the car is turning left?

The F in F = mv^2/r is the force in the direction of the center of the turning circle. The friction force is in that direction, so it is positive. I don't think you want to confuse things by thinking about left and right when the essential direction is centripetal - toward the center.

the book says the radial component is simply the magnitude of the vector...so in doing probs with uniform circular motion, where a is pointing towards the center...it is positive regardless of where it points in the free body diagram?

Yes, positive as long as it points toward the center.

thank you

1. What is uniform circular motion?

Uniform circular motion is the motion of an object moving in a circular path at a constant speed. This means that the object is traveling in a circular path with the same speed and direction at all times.

2. How do you calculate the velocity of an object in uniform circular motion?

The velocity of an object in uniform circular motion can be calculated by dividing the distance traveled around the circle by the time it takes to make one complete revolution. This is also known as the circumference divided by the period.

3. What is the difference between angular velocity and tangential velocity?

Angular velocity refers to the rate at which an object rotates around a central point, while tangential velocity refers to the speed of the object in a circular path. Angular velocity is measured in radians per second, while tangential velocity is measured in meters per second.

4. How does the centripetal force affect an object in uniform circular motion?

The centripetal force is the force that keeps an object moving in a circular path. It acts towards the center of the circle and is responsible for changing the direction of the object's velocity, but not its speed. Without this force, the object would move in a straight line instead of a circular path.

5. Can an object in uniform circular motion have a changing speed?

Yes, an object in uniform circular motion can have a changing speed if the radius of the circle it is traveling in changes. This would result in a change in the magnitude of the centripetal force, which would cause a change in the speed of the object.

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