Circular Motion

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Circular Motion - PowerPoint PPT Presentation

Circular Motion. Measuring a Circle. Motion in a circle is common. The most important measure is the radius ( r ). We use degrees to measure position around the circle. There are 2 p radians in the circle. This matches 360 °

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PowerPoint Slideshow about 'Circular Motion' - rolanda

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Presentation Transcript

Circular Motion

Measuring a Circle
• Motion in a circle is common.
• The most important measure is the radius (r).
• We use degrees to measure position around the circle.
• There are 2p radians in the circle.
• This matches 360°
• The distance around a circle is s = rq, where q is in radians.

s = r q

q

r

Period and Frequency
• Movement around a circle takes time.
• The period (T) is the time it takes to complete one revolution around the circle.
• The frequency (f) is the number of cycles around completed in a time.
• Cycles per second (cps or Hz)
• Revolutions per minute (rpm)
• Frequency is the inverse of period (f = 1/T).
Velocity in a Circle
• Velocity is a vector change in position compared to time.
• The small change in position on the path is the radius times the change in angle.
• The magnitude rate of change is

Dr = r Dq

Dq

r

Angular Velocity
• For circular motion, only the time rate of change of the angle matters.
• The time rate of change of the angle is called the angular velocity.
• Symbol (w)
• Units (rad/s or 1/s = s-1)
Frequency is measured in cycles per second.

There is one cycle per period.

Frequency is the inverse of the period, f =1/T.

Angular velocity is measured in radians per second.

There are 2p radians per period.

Angular velocity, w = 2p/T.

Angular velocity, w = 2pf.

Direction of Motion
• In the limit of very small angular changes the velocity vector points along a tangent of the circle.
• This is perpendicular to the position.
• For constant w, the magnitude stays the same, but the direction always changes.
Acceleration in a Circle
• Acceleration is a vector change in velocity compared to time.
• For small angle changes the acceleration vector points directly inward.

dq

Centripetal Acceleration
• Uniform circular motion takes place with a constant speed but changing velocity direction.
• The acceleration always is directed toward the center of the circle and has a constant magnitude.
• This is called centripetal acceleration.

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