Uniform Circular Motion http://www.physicsclassroom.com/mmedia/circmot/circmotTOC.html

Uniform circular motion motion of an object in a circle with a constant or uniform speed constant change in direction

Centrifugal vs Centripetal Centrifugal force represents the effects of inertia that arise in connection with rotation and which are experienced as an outward force away from the center of rotation. Centripetal force is a force that makes a body follow a curved path towards a point as to a center What we will use is centripetal force

Uniform Circular Motion: Period Object repeatedly finds itself back where it started. The time it takes to travel one “cycle” is the “period”.

Quantifying Acceleration: Magnitude v1 v2

Quantifying Acceleration: Magnitude Centripetal Acceleration

Applying Newton’s 2nd Law: Centripetal Force Always points toward center of circle. (Always changing direction!) Centripetal force is the magnitude of the force required to maintain uniform circular motion.

Direction of Centripetal Force, Acceleration and Velocity Without a centripetal force, an object in motion continues along a straight-line path.

Direction of Centripetal Force, Acceleration and Velocity

What if velocity decreases?

What if mass decreases?

What if radius decreases?

What provides the centripetal force? Tension Gravity Friction Normal Force Centripetal force is NOT a new “force”. It is simply a way of quantifying the magnitude of the force required to maintain a certain speed around a circular path of a certain radius.

Relationship Between Variables of Uniform Circular Motion Suppose two identical objects go around in horizontal circles of identical diameter but one object goes around the circle twice as fast as the other. The force required to keep the faster object on the circular path is the same as one fourth of half of twice four times the force required to keep the slower object on the path. The answer is E. As the velocity increases the centripetal force required to maintain the circle increases as the square of the speed.

Relationship Between Variables of Uniform Circular Motion Suppose two identical objects go around in horizontal circles with the same speed. The diameter of one circle is half of the diameter of the other. The force required to keep the object on the smaller circular path is the same as one fourth of half of twice four times the force required to keep the object on the larger path. The answer is D. The centripetal force needed to maintain the circular motion of an object is inversely proportional to the radius of the circle. Everybody knows that it is harder to navigate a sharp turn than a wide turn.

Relationship Between Variables of Uniform Circular Motion Suppose two identical objects go around in horizontal circles of identical diameter and speed but one object has twice the mass of the other. The force required to keep the more massive object on the circular path is the same as one fourth of half of twice four times Answer: D.The mass is directly proportional to centripetal force.

Tension Can Yield a Centripetal Acceleration: If the person doubles the speed of the airplane, what happens to the tension in the cable? Doubling the speed, quadruples the force (i.e. tension) required to keep the plane in uniform circular motion.

Friction Can Yield a Centripetal Acceleration:

Car Traveling Around a Circular Track Friction provides the centripetal acceleration

Friction Can Yield a Centripetal Acceleration W FN fs Force X Y W -mg FN fs -sFN Sum ma What is the maximum speed that a car can use around a curve of radius “r”?

Maximum Velocity Force X Y W -mg FN FC -sFN Sum ma

Centripetal Force: Question A car travels at a constant speed around two curves. Where is the car most likely to skid? Why? Smaller radius: larger force required to keep it in uniform circular motion.

Gravity Can Yield a Centripetal Acceleration: Hubble Space Telescope orbits at an altitude of 598 km (height above Earth’s surface). What is its orbital speed?

Gravity and Centripetal Acceleration: Centripetal acceleration provided by gravitational force

Gravity and Centripetal Acceleration: Solve for the velocity….

Hubble Space Telescope:

Banked Curves Why exit ramps in highways are banked?

Banked Curves Q: Why exit ramps in highways are banked?

Banked Curves Q: Why exit ramps in highways are banked? A: To increase the centripetal force for the higher exit speed.

The Normal Force Can Yield a Centripetal Acceleration: Engineers have learned to “bank” curves so that cars can safely travel around the curve without relying on friction at all to supply the centripetal acceleration. How many forces are acting on the car (assuming no friction)?

Banked Curves Why exit ramps in highways are banked? FN cosq = mg

Banked Curves Why exit ramps in highways are banked? FN cosq = mg

The Normal Force as a Centripetal Force: Two: Gravity and Normal Force X Y W -mg FN FNsin FNcos Sum ma

The Normal Force as a Centripetal Force:

The Normal Force and Centripetal Acceleration: How to bank a curve… …so that you don’t rely on friction at all!!

Artifical Gravity

Vertical Circular Motion

Vertical Circular Motion

Calculations Practice Set 1 – link Practice Set 2 - link

Acknowledgements http://www.physicsclassroom.com/mmedia/circmot/ circmotTOC.html

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