Uniform Circular Motion: Understanding the Characteristics and Misconceptions

[needhelpfast]

Homework Statement

Which, if any, of the following statements about a particle in uniform circular motion is/are true?
Its acceleration vector is a constant.
Its velocity and acceleration vectors are always perpendicular.
The direction of its acceleration is toward the center of rotation.
The magnitude of its acceleration is a constant.
Its velocity vector is a constant.
Its velocity and acceleration vectors are always parallel.
Its speed is constant.

Homework Equations

The Attempt at a Solution

I thought that the answers were true, true, true, true, false, false, true, but this was wrong, and I don't understand why?

 

[PhanthomJay]

You only got one wrong. Hint: Think about vectors.

 

[needhelpfast]

is it false that velocity vectors and acceleration vectors are always perpendicular? because the velocity vector is changing?

 

[jobsism]

The first is false, since at each instant of motion, the body is changing its position, and so the direction of acceleration changes with respect to the previous position, BUT all of them are directed towards the centre.

The second is true, since the direction of velocity vector acts tangential to the rotatory motion.

The third is true, as centripetal acceleration is always directed towards the centre.

The fourth is true, as centripetal acceleration, a=v^2/r, and since magnitude of velocity is a constant, so is acceleration.

The fifth is false, as at each instant of motion, the direction of velocity vector changes.

The sixth is utterly false, as they are always perpendicular.

The seventh is true, as the magnitude of velocity, which can be considered as speed, is constant in uniform circular motion.

So, only the first is wrong for you.

 

[needhelpfast]

thank you!