# How do you prove #a=v^2/r# and #a=r\omega^2# using a circle and vector diagram?

##
I know you start off with a circle and two points on the circumference. Each point has an arrow tangent to the circle and are facing the same way (in terms of rotation).

Then, you connect the two points to the center, and label each line #r# , and the angle between them #\theta# .

The vector diagram has the two arrows connected tail to tail, with an angle of #\theta# . An arrow is drawn from head to head, and is the force provided (#abs(v_1)+abs(v_2)# ). It also has something to do with #sin\theta=\theta# for very small angles or something similar.

I'm not sure where to go from there.

Please do not use derivative, and other vector stuff. Also include diagrams.

I know you start off with a circle and two points on the circumference. Each point has an arrow tangent to the circle and are facing the same way (in terms of rotation).

Then, you connect the two points to the center, and label each line

The vector diagram has the two arrows connected tail to tail, with an angle of

I'm not sure where to go from there.

Please do not use derivative, and other vector stuff. Also include diagrams.

See the expplanation below

The acceleration is

The angular velocity is

Addition

For small angles

Dividing by

By signing up, you agree to our Terms of Service and Privacy Policy

To prove ( a = \frac{v^2}{r} ) and ( a = r\omega^2 ) using a circle and vector diagram, we can utilize the relationship between linear and angular quantities in circular motion. By considering the motion of an object undergoing uniform circular motion, we can analyze the forces acting on it and apply Newton's laws of motion.

By signing up, you agree to our Terms of Service and Privacy Policy

- An object with a mass of #5 kg# is revolving around a point at a distance of #3 m#. If the object is making revolutions at a frequency of #7 Hz#, what is the centripetal force acting on the object?
- A hailstone falls from a height of #5# #km#. Ignoring air resistance, what is the hailstone's final velocity? The acceleration due to gravity is #9.8# #ms^-2#.
- A model train, with a mass of #6 kg#, is moving on a circular track with a radius of #1 m#. If the train's kinetic energy changes from #27 j# to #36 j#, by how much will the centripetal force applied by the tracks change by?
- An object with a mass of #6 kg# is revolving around a point at a distance of #4 m#. If the object is making revolutions at a frequency of #1 Hz#, what is the centripetal force acting on the object?
- A box with a mass of 14.8 kg sits on the floor. How high would you have to lift box to for it to have a gravitational potential energy of 355 J?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7