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3.1 Uniform Circular Motion
Physics 30Unit 3 Circular Motion
Lesson 3.1 Outline• Uniform Circular Motion• Centripetal Acceleration• Tangential Velocity• Examples
You will be able to:• define uniform circular
motion• predict directions of
objects motion when circular motion stops
• solve problems involving centripetal acceleration
• analyze the circular path of an object and predict direction of acceleration and velocity
What is Uniform Circular Motion?Uniform Circular Motion is motion that occurs in a circular path at a constant speed. This is not the same as a constant velocity. As the object travels around the circular path, the magnitude of the velocity is constant (speed), but the direction is constantly changing.
3.1 Uniform Circular Motion
As the object travels around the circular path, the magnitude of the velocity is constant (speed), but the direction is constantly changing. This means the velocity is changing!
If velocity is changing, there must be an acceleration.
vv
vv
Centripetal Acceleration
velocity
accelerationCentripetal acceleration is directed towards the center of the circle.
Velocity is tangential to the circular path.
Velocity and centripetal acceleration are perpendicular.A tangent line only
touches a circle at a single point.
3.1 Uniform Circular Motion
Things to remember about circular motion• There are 360 degrees or 2π radians in one revolution• The distance an object travels in a circular path is the circumference of the
circle for one full revolution• Speed is constant• Velocity is not, because direction changes• Centripetal acceleration changes the velocity
ac =v2r
Speed or magnitude of velocity
Centripetal Acceleration
Radius
If you increase the radius, the centripetal acceleration gets smaller. It takes less acceleration to change the direction, because the direction doesn't change as fast. If you increase the speed, it increases the centripetal acceleration because it takes more acceleration to change the direction of an object moving at high speed.
3.1 Uniform Circular Motion
The distance around a circle is the circumference and is equal to 2πr, where r is the radius. If we consider T the time it takes for a single revolution (sometimes called the period), the velocity (v) can be calculated using this formula.
v = 2πrT
Another useful formula
A ball is swung in a horizontal circle that has a velocity of 3.0 m/s and a radius of 0.40 m. Another ball is swung in a horizontal circle that has a velocity of 3.2 m/s and a radius of 0.60 m. Which undergoes a greater acceleration?
3.1 Uniform Circular Motion
A car is moving with a constant velocity around a circular path. If the radius of the circular path is 48.2 m and the centripetal acceleration is 8.05 m/s2 , what is the tangential speed of the car?
A car travels around a circular track that changes the odometer from 200124.3 km to 200125.6 km at 35.0 m/s after 1 revolution. What is the centripetal acceleration? How long does a revolution take?
3.1 Uniform Circular Motion
A rock is attached to a 0.500 m long string. The rock makes one revolution in 2.00 seconds. What is the tangential velocity of the rock? What is the acceleration of the rock?