1. Circular Motion Uniform circular motion: examples include
Objects in orbit (earth around the sun
Driving a car around a corner
Rotating a ball around on a string

2. Circular Motion c

3. Circular Motion
According to Newton’s mechanics, objects don’t tend to move in a circle by themselves. They tend to either be at rest of move in a straight line at constant speed (this is Newton’s first law)

4. Circular Motion Circular motion is not “natural” motion
Something (a Force) must make an object move in a circle
The Force causing circular motion can be one of many different forces, depends on the situation (orbit = gravitational force, car turning a corner = frictional force between tires and the road, ball on a string = tension force)

5. Circular motion
example

6. Circular motion: car travelling around a corner
F is friction

7. Example of circular motion
Now gravity is influencing circular motion

8. Circular Motion
Remember from Newton’s 2nd law, that …..Force = mass x acceleration (F = ma)
But if the object is in uniform circular motion, their speed is constant, so is acceleration = 0?

9. Circular Motion
In circular motion, the acceleration is a change in the direction of the object, even though the speed is constant, the direction keeps changing, and velocity is a vector.
The force keeps pulling the object to the center, hence we call this type of acceleration “centripetal” acceleration which means “center seeking”.

10. Circular Motion
Solving circular motion problems is like a typical “force” problem where the motion is circular rather than linear.
F = ma still works, now we have a new term for centripetal acceleration
ac = v2/r acceleration (centripetal) = velocity squared/radius.

11. Uniform circular motion
Centripetal acceleration

12. Circular Motion Example ….. Ball on a string rotating horizontally
Let’s say it’s a 1 kg ball rotating at 4 m/s at a radius of 0.5m. What is the Force of tension in the string?
Find the acceleration of the ball where a = v2/r
Using the idea that F=ma and that the Force causing circular motion is the tension in the string.