CIRCULAR MOTION

Mr. Theuerkauf

CIRCULAR NOTES

Axis – the line or point around which an object rotates. Rotation: spinning around an

internal axis Example: The Earth rotates

around its axis once every 24 hours (1 day).

Revolution: Moving around an external axis Example: The Earth revolves

around the sun once every 365.25 days (1 year).

MORE ABOUT CIRCULAR MOTION

Period – the amount of time it takes for ONE rotation or revolution.

Unit: seconds (s)

Frequency – the number of rotations or revolutions per second.

Unit: Hertz (Hz)

Period and frequency are inverse (reciprocals).

€

v =2Πr

T=C

T

€

f =# revolutions(rotations)

# seconds

€

T =1

f

€

f =1

T

LINEAR VELOCITY

Linear Velocity – the distance moved per unit time

Always drawn tangent to the circular path.

Direction is the direction the object wants to move (inertia – wants to move in a straight line)

Distance = circumference (C) C = 2πr

Time = time for one revolution = Period (T)

Tangential Velocity depends on how far away the object is from the center of the circle (radius)

At the center, v = 0 m/s b/c r = 0As you move away from the center,

radius increases so your tangential velocity increases

€

v =2Πr

T=C

T

ROTATIONAL VELOCITY

Rotational Velocity – the number of rotations per unit time Depends on the number of degrees you turn in a

given amount of time Does NOT depend on where you stand (radius)

because the distance traveled (angle) will be the same

DIRECTLY proportional to tangential velocity. The faster the object turns (rotational velocity) the

fater the tangential velocity will be.

CENTRIPETAL ACCELERATION

When an object moves in a circle, direction is constantly changing. Therefore, the velocity is constantly changing. The object is ACCELERATING.

Centripetal Acceleration – the acceleration due to an object moving in a circular path; constantly changing velocity

Unit: m/s2

Direction is always towards the center of the circle

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ac =v 2

r

CENTRIPETAL FORCE – THE NET FORCE CAUSING CIRCULAR MOTION

Units: N

Direction of Fc is always into the center of the circle; like ac.

Fc is not an additional force; it is just the net force that is causing the object to keep changing direction.

Examples: tension in a string, the wall of a salad spinner.

If Fc is removed, the object will fly off in the direction of the tangential velocity (straight line).

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Fc = Fnet = mac =mv 2

r

TORQUE

A net torque produces ROTATION Torque (τ): The ability of a force to cause an

object to rotate. More torque means the object will rotate more easily.

Axis of rotation: the invisible line around which an object rotates. Examples: your elbow, the hinge of a door.

TORQUE DEPENDS ON…

1. The amount of force exerted2. The distance between the force and the

axis of rotationLever Arm – the distance between the applied force and the axis; measured in meters.

Example: Using a wrench. Hold close to bolt, it’s harder to turn than when you hold farther away. Greater lever arm, greater torque, easier to turn.

3. The angle that the force is applied. Perpendicular is best.