Circular Motion

KCHS Physics

What is circular motion?

Anything that rotates or revolves around a central axis is in circular motion.

Rotation vs. Revolution

When an object turns about an internal axis—that is, an axis located within the body of the object—the motion is called rotation, or spin.

When an object turns about an external axis, the motion is called revolution.

An axis is the straight line around which rotation takes place.

Rotation vs. Revolution

The Ferris wheel turns about an axis.

The Ferris wheel rotates, while the riders revolve about its axis.

Rotation vs. Revolution

The turntable rotates around its axis while a ladybug sitting at its edge revolves around the same axis.

Conditions for Uniform Circular Motion

An object moving in uniform circular motion has constant speed but not constant velocity because the direction is changing.

The velocity vector is tangent to the circle, and the acceleration is along a radius of the circle.

Conditions for Uniform Circular Motion

The velocity vector and the acceleration vector are always perpendicular to each other.

The acceleration vector changes only the direction of the velocity vector not the magnitude of it.

Conditions for Uniform Circular Motion

A

V

Circular Motion Formulas

v = tangential speed (m/s)

r = radius of circle (m)

T = period or time for one revolution

(sec)

T

rv

2

Formulas

ond

srevolutionf

srevolution

ondsT

sec

sec

T = period or time for one revolution (sec)

f = frequency or revolutions per second (Hz or sec-1)

Formulas

T = period or time for one revolution (sec)

f = frequency or revolutions per second (Hertz or

sec-1)

Tf

1

Formulas

ac = centripetal acceleration (m/s2)

r = radius of circle (m)

v = tangential speed (m/s) a

v

rc 2

Sample Problem

A little girl is swinging her 5 kg purse in horizontal circles using the strap that allows the purse to swing 20 cm from her hand. The girl is able to get the purse to make 10 revolutions in 8 seconds. A) What is the period of the purse? B) What is the tangential speed of the purse? C) What is the centripetal acceleration of the

purse?

Givens:Givens: Formula:Formula: Answer:Answer:

Work:Work:

Unknown:Unknown:

10 revolutions10 revolutions

8 seconds8 seconds

T = T = 8 seconds 8 seconds 10 revolutions10 revolutions

T = T = seconds seconds revolutionsrevolutions T = 0.8 sec/revT = 0.8 sec/rev

A) What is the period of the purse?

T = ?

Givens:Givens: Formula:Formula: Answer:Answer:

Work:Work:

Unknown:Unknown:

T = 0.8 sec/revT = 0.8 sec/rev

R = 20cm = 0.2mR = 20cm = 0.2m

V = V = 2 2ππ (0.2 m) (0.2 m) 0.8 sec/rev0.8 sec/rev

V = 2V = 2ππr / Tr / T V = 1.57 m/s V = 1.57 m/s

B) What is the tangential speed of the purse?

V = ?

Givens:Givens: Formula:Formula: Answer:Answer:

Work:Work:

Unknown:Unknown:

V = 1.57 m/sV = 1.57 m/s

R = 20cm = 0.2mR = 20cm = 0.2m

aacc = = (1.57 m/s) (1.57 m/s)22

0.2 m0.2 m

aacc = 12.32 m/s = 12.32 m/s22

C) What is the centripetal acceleration of the purse?

ac = ?

av

rc 2

Frame of Reference

A frame of reference is a system for describing the locations of objects. It is used to specify the positions and relative motions of objects.

Inertial frame of reference (non accelerating)- Newton’s first law holds true. i.e. watching an Indy race from the grand stands.

Frame of Reference

Accelerating frame of reference - Newton’s first law does not hold true. i.e. watching an Indy race from the point of view of the driver.

In an accelerating frame of reference (inside the car), as the car goes around a corner, the passengers think they feel a force towards the outside of the curve, in reality this is inertia.