1. Circular Motion and Other Applications of Newton’s Laws
Chapter 6
Circular Motion
and
Other Applications of Newton’s Laws

2. Uniform Circular Motion
A force, Fr , is directed toward the center of the circle
This force is associated with an acceleration, ac
Applying Newton’s Second Law along the radial direction gives

3. Uniform Circular Motion, cont
A force causing a centripetal acceleration acts toward the center of the circle
It causes a change in the direction of the velocity vector
If the force vanishes, the object would move in a straight-line path tangent to the circle

4. Centripetal Force
The force causing the centripetal acceleration is sometimes called the centripetal force
This is not a new force, it is a new role for a force
It is a force acting in the role of a force that causes a circular motion

5. Forces that causes centripetal acceleration
We are familiar with different types of forces such as
Gravity, friction, normal forces and tension etc.
Should we add centripetal forces in this list?
Answer: No, It is not new kind of force.
A common mistake in the free body diagram is to draw all usual forces and then to add another vector for the centripetal force.
But it is not a separate force---it is simply one or more familiar forces that causes circular motion

6. Examples Motion of the earth around the sun: Gravitational force
An Object sitting on rotating turn table: Friction force
The rock whirled horizontally on the end of string: Tension in the string
For an amusement-park Patron pressed against the inner wall of rapidly rotating room: normal force exerted by the wall

7. Conical Pendulum
The object is in equilibrium in the vertical direction and undergoes uniform circular motion in the horizontal direction
v is independent of m

8. The conical Pendulum

9. Motion in a Horizontal Circle
The speed at which the object moves depends on the mass of the object and the tension in the cord
The centripetal force is supplied by the tension

10. How fast can it spin
The force cause to the centripetal acceleration is the tension in the string

11. Horizontal (Flat) Curve
The force of static friction supplies the centripetal force
The maximum speed at which the car can negotiate the curve is
Note, this does not depend on the mass of the car

12. What is the maximum speed of the car?
The static friction force enable the car to move round the circular path

13. Banked Curve These are designed with friction equaling zero
There is a component of the normal force that supplies the centripetal force

14. The Bank Exit Ramp

16. Loop-the-Loop This is an example of a vertical circle
At the bottom of the loop (b), the upward force experienced by the object is greater than its weight

17. Loop-the-Loop, Part 2
At the top of the circle (c), the force exerted on the object is less than its weight