1. Uniform Circular Motion
AP Physics
Sections 5-1 to 5-3
Uniform Circular Motion

2. Circular motion
An object with mass moves in a circle with a constant speed.
This is uniform circular motion.
The velocity vectors at time 1 and 2 are the same length, but point in different directions.
An object with mass moves in a circle with a constant speed.
This is uniform circular motion.
The velocity vectors at time 1 and 2 are the same length, but point in different directions.
During the same time interval ∆t, the radius also acts as a vector, and sweeps out an angle. It changes direction, but not its size, just like the velocity vector.
The angle change for ∆v is exactly the same as for ∆r.
During the same time interval ∆t, the radius also acts as a vector, and sweeps out an angle. It changes direction, but not its size, just like the velocity vector.
The angle change for ∆v is exactly the same as for ∆r.
During the same time interval ∆t, the radius also acts as a vector, and sweeps out an angle. It changes direction, but not its size, just like the velocity vector.
The angle change for ∆v is exactly the same as for ∆r.
During the same time interval ∆t, the radius also acts as a vector, and sweeps out an angle. It changes direction, but not its size, just like the velocity vector.
The angle change for ∆v is exactly the same as for ∆r.

3. The triangles are similar. Since |r1| = |r2| and |v1| = |v2|
∆r = r2 - r1
∆v = v2 - v1
The triangles are similar.
Since |r1| = |r2| and |v1| = |v2|
We can simply write r and v.
The triangles are similar.
Since |r1| = |r2| and |v1| = |v2|
We can simply write r and v.
We can write the ratio equation: ∆v / v = ∆r / r
For very small time intervals, the angle θ is small, and ∆r approximates the arc of the path. The speed is therefore, v = ∆r/∆t.
For very small time intervals, the angle θ is small, and ∆r approximates the arc of the path. The speed is therefore, v = ∆r/∆t.

4. Centripetal acceleration
Centripetal means “center seeking.”
It is the acceleration causing the velocity’s direction to change.
Centripetal means “center seeking.”
It is the acceleration causing the velocity’s direction to change.
If v = ∆r/∆t then ∆r = v ∆t
Substituting this into our ratio equation:
∆v/v = ∆r/r
∆v/v = v ∆t/r
∆v = v2 ∆t/r
∆v/∆t = v2/r
ac = v2/r

5. ac in terms of period
The period, T, is the time in seconds to revolve around the circle once.
The period, T, is the time in seconds to revolve around the circle once.
The period, T, is the time in seconds to revolve around the circle once.
The object moves through the circumference distance 2πr during period T.
The object moves through the circumference distance 2πr during period T.
Speed around the whole circle is 2πr/ T.
ac = (2πr/ T )2/r
ac = 4π2r/ T2

6. Centripetal force
Using Newton’s second law:
Fc = mac ac Fc

7. Non-Newtonian forces
Objects revolving or rotating are accelerating frames of reference.
Objects revolving or rotating are accelerating frames of reference.
Objects revolving or rotating are accelerating frames of reference.
Objects inside accelerating frames of reference can seem to violate Newton’s laws.
Objects inside accelerating frames of reference can seem to violate Newton’s laws.
In reality, the law of inertia creates these fictional forces.
In reality, the law of inertia creates these fictional forces.
“F” Fc
centripetal force
“centrifugal
force” ac
Real force inward.
Objects inside the car feel a “force” outward. v
Object on dashboard continues in straight line motion!

8. What force keeps the car in the curve without slipping?
What keeps the car in the curve in this diagram?
Static friction.
The inward component of the normal force.
(For an ideal banked curve.)
On a real banked curve, both static friction and the normal force act.