Circular Motion

Uniform Circular Motion

• Motion of an object at constant speed along a circular path

Velocity is changingr1

r2

Radius – Measured in meters

v1v2

If Velocity is changing, then it must be accelerating!

Velocity• Velocity vector is always tangent to the

curve of the circle in the direction of the motion

• (Imagine what would happen if you let go, where would the object go?)

Acceleration Equation:

ac = v2 /r

ac = centripetal acceleration (m/s2)

v = velocity (m/s)r = radius (m)

Newton’s Second Law

• When an object undergoes a constant acceleration, there must be a constant force acting upon it.

• Centripetal Force

F = m a

ac =v2 /rv2 /r

Centripetal

• Centripetal means center seeking.• So centripetal force and acceleration

are always center seeking

Fc

Recap

• ac = v2 /r

• Fc = mv2 / r• Force and Acceleration are pointing

towards the center• Velocity is tangent to the curve

CAREFUL!!!

• Common MisconceptionCentriPETAL – Towards CenterCentriFUGAL – Away from center

- Doesn’t actually “exist.” - It is used to describe the apparent outward

force that you feel. - This force is because of Newton’s Third Law: For every force there is an equal and opposite force.

Example

• An object with mass of 5.0 kg moves in a circular path of radius .50 m at a speed of 10 m/sa) Calculate the centripetal accelerationb) Calculate the centripetal force

Answer: a) 2.0 x 102 m/s b) 1.0 x 103 N

On Your Own

• A 10 kg object moves in a circular path of radius 9 m with a velocity of 4 m/s. a) Find the centripetal acceleration of the objectb) Find the centripetal force on the object

1. A 5 kg object moves in a circular path of radius 2 m with a velocity of 6 m/s. a) Find the centripetal acceleration of the objectb) Find the centripetal force on the object

2. Draw an object going around in a circle. Label the velocity vector, force vector and acceleration vector (Which way will they be pointing?)

HAND IN

• Linear Speed – Speed in a straight line, distance over time

• Tangential Speed – Speed in a circle, velocity is tangent to the curve

• Rotational Speed - # of Rotations per amount of time