Physics Lesson 11/1o

Physics Lesson 11/1o

Circular Motion

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Journal - Chop Wood Carry Water

Time to go Round and Round

A little 80's throwback to get us started.

Observe

Disclaimer - I am not responsible for any injuries that occur due to flying objects.

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As I swung the mass around my head at a constant speed, was it accelerating?

Yes, it was, acceleration is not a change in speed, but in velocity.

You can change either the speed or the direction in order to accelerate!

Uniform Circular Motion

• the movement of an object at a constant speed around a circle with a fixed radius.

• The position of an object in uniform circular motion, relative to the center of the circle, is given by the position vector, r.

• Remember that a position vector is a displacement vector with its tail at the origin.

Uniform Circular Motion

• Two position vectors r₁ and r₂, at the beginning and ending of a time interval are shown in the left image.

• As the object moves around the circle, the length of the position vector does not change, but its direction does.

• The diagram also shows two instantaneous velocity vectors that are tangent to circular path at right angles to the position vectors.

Uniform Circular Motion

• To determine the object's velocity, you need to find it's displacement over a time interval.

• If you recall, a moving object's velocity is

   $\frac{\Delta x}{\Delta t}$  

• So far an object in circular motion  $\nu=\frac{\Delta r}{\Delta t}$  

Uniform Circular Motion

• The right side of the image shows Δr drawn as the displacement from r₁ to r₂ during a time interval.

• The velocity for this time interval has the same direction as the displacement, but its length would be different because it is divided by Δt.

Centripetal Acceleration

You just learned that the velocity vector of an object in uniform circular motion is tangent to the circle. So what is the direction of the acceleration?

Centripetal Acceleration

• The image to the right shows the velocity vectors at the beginning and the end of a time interval.

• The difference in the two vectors (Δv) is found by subtracting the vectors, as shown at the bottom of the picture.

Centripetal Acceleration

• The average acceleration 

   $a=\frac{\Delta v}{\Delta t}$ , is the same direction as  $\Delta v$  

• For a very small time interval,  $\Delta v$  is so small tha  $a$  points toward the center of the circle.

Centripetal Acceleration

• Repeat this process for several other time intervals when the object is in different locations on the circle.

• As the object moves around the circle, the direction of the acceleration vector changes, but it always points to the center of the circle.

Centripetal Acceleration

• The word centripetal means center seeking.

• Since the acceleration is always pointing to the center, the acceleration of an object in uniform circular motion is referred to as centripital acceleration.

Tomorrow, we continue to discuss Centripetal Acceleration.

Open Ended

What direction does the acceleration of an object in uniform circular motion always point?