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

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)

Example of circular motion  Bucket on string

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)

Circular Motion  Remember from Newton’s 2 nd 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?

 Objects in circular motion require a Force!

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”.

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  a c = v 2 /r acceleration (centripetal) = velocity squared/radius.

Circular Motion  Example ….. Ball on a string rotating horizontally  Let’s say it’s a 3 kg ball rotating at 5 m/s at a radius of 2m. What is the Force of tension in the string?  Find the acceleration of the ball where a = v 2 /r  Using the idea that F=ma and that the Force causing circular motion is the tension in the string.