Centripetal Force

Centripetal Force Inwardly directed force which causes a body to

turn; perpendicular to velocity

Centripetal force always arises from other forces, and is not a unique kind of force Sources include gravity, friction, tension,

electromagnetic, normal

ΣF = ma

a = v2/r

ΣF = m v2/r

Oh Centrifugal Force, you faker

Oh Centrifugal Force, you faker

How does it feel when you are riding in a car that makes a sharp turn?

There is not actually an outward force (centrifugal force)

What you are feeling is the inertia of your body – trying to maintain continuous motion

This is true of all circular motion

How does it feel when you are riding in a car that makes a sharp turn?

There is not actually an outward force (centrifugal force)

What you are feeling is the inertia of your body – trying to maintain continuous motion

This is true of all circular motion

Linear / Angular SpeedA young boy and girl are sitting on a Merry-go-

Round – the girl sits on the edge, and the boy sits near the axle. Which person has a higher speed?

v=2r/T (m/s) = rotations/time (rad/s)

v=rPeriod – time for one complete cycle

Frequency = cycles / time

Example: Highway Curves

R

r

z

Friction turns the vehicle

Normal force turns the vehicle

Practice Problem:

A 1500 kg car is navigating a curve on a flat road. The radius of the curve is 35.0 m and the coefficient of static friction b/w the tires and the road is .500. Find the maximum speed of the car so it can still make the curve without sliding off the road.

Practice Problem:

In a circus performance, Allo “Dare Devil” Diavolo introduced the stunt of riding a bicycle in a loop-the-loop. Assuming that the loop is a circle with radius R=2.7 m, what is the least speed v Diavolo could have a the top of the loop to remain in contact with it there?

Conical Pendulum

What provides the centripetal force for a conical pendulum?

z

r

T

mg

L

PHUN PHYSICS QUIZ: Derive an expression for the velocity of a conical pendulum with respect to the string length and angle θ.

z

r

T

mg

L

θ

Practice Problem:

An engineer is designing a rounded exit ramp for a highway. The ramp is to be made so that a car wouldn’t have to rely on friction to round the curve without skidding (like when it’s icy). To do this the ramp must be banked, or tilted toward the center of the curve. The radius of the curve is 50.0 m and the speed limit on the ramp is 13.4 m/s (30 mph).

At what angle should the ramp be banked?