Circular Motion: IN-CLASS REVIEW

Circular Motion: IN-CLASS REVIEW

Basic Circular Motion Equations:

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You need to know how to get the centripetal acceleration and the centripetal force in terms of T (period) instead of v (velocity):

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Things to Remember for BASIC CIRCULAR MOTION:

Concept #1: If an object travels in a circle, it does so against its will. It wants to move in a straight line.

Concept #2: The velocity of an object that travels in a circular path is TANGENT to the circle, at every moment in time.

Concept #3: Objects that move in a circular path, even those that are traveling at a constant velocity, are in fact accelerating.

Concept #4: The acceleration of an objects moving in circular path is always directed INWARD (but not just “inward”, rather “inward towards the center of the circular path”). This acceleration is called the CENTRIPETAL acceleration, which mean “center-seeking”.

Concept #5: There is no such thing as a CENTRIFUGAL force. Things appear to “pull” outward b/c of their inertia. They want to continue in the direction in which they are traveling at any given moment (tangent to the circle, in a straight line).

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Things to Remember for HORIZONTAL circles:

Always ask the question “What supplies the centripetal force?”
If a force points into the circle, it’s a WINNER.
If a force points out of the circle, it’s a LOSER.
“Winners – Losers = FNet“ (or, more helpful in this chapter, “INs – OUTs = FC”)
Things that supply Fc: Ff (= FN), Tension, force of adhesion, force of attraction, etc

Things to Remember for VERTICAL circles:

* Apparent Weight and Normal Force mean the same thing.

** When talking about a maximum tension or “pulling” max # of g’s, use the bottom equation.

*** T, FN, and FL go to zero at the top when moving at the critical velocity.

Things to remember for BANKED TURNS (and SWING RIDES):

Woop-de-doos

Know your GR’s (grrrrrrrrrrrrrr……)

Circular Motion: OUT-OF-CLASS REVIEW

This review packet should prepare you well for the uniform circular motion exam. In fact, it should be a little bit harder than the test itself. If you have trouble on a particular problem, look at similar HW problems (from previous assignments) and/or look at the online Powerpoint Review. Make sure to draw free-body-diagrams (FBDs) for each problem.

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A circular turntable turns at a speed of 40 rev/min. A 3-gram ant sits 6 cm away from the center of rotation. Find:

a)the period of the turntable.

b)the force of friction that keeps the ant moving in the circular path.

c)The minimum coefficient of friction that will provide this centripetal force.

A 30 g ball on a 45 cm string is swung in a horizontal circle above the head of a physics student. If 10 revolutions take 7 seconds, find the tension in the string.

Another physics student, who isn’t the best “cowboy” swings his ball (again of mass 30g on a string of length 45cm) in a “less-than-horizontal” manner (instead, it looks more like a conical pendulum with a angle of 10o between the horizontal and the string). After drawing a detailed FBD of the situation, find….

a)the tension in the string.

b)the radius of the circle that the ball actually travels.

c)the velocity of the ball.

d)the time necessary to complete 10 revolutions.

A 1500 kg truck travels around a flat circular turn at 25 m/s. If the turn’s radius is 100 m, find the minimum coefficient of friction that will keep this car from sliding.

If the 1500 kg truck travels at 20 m/s around a circular turn with 20o banked turns, find the radius of the turn that will keep the car from sliding up or down the embankment.

A ball is swung around in a vertical circle by a string that is 30 cm long. If the tension in the string is 20 N at the top of the circular path, and the ball’s period is .25 seconds, find the mass of the ball.

What would be the minimum velocity necessary to keep the ball from problem #6 above in the same circular path?

A stunt biker goes through a loop-de-loop of radius 2 m. If the biker’s (w/ the bike) total mass is 300 kg, find the constant speed that would produce an apparent weight at the bottom of the loop of 3 times his regular weight.

What would be the minimum velocity necessary to keep the biker from problem #8 above from losing contact with the track at the top of the loop?

A plane is traveling at 300 m/s in a vertical, circular loop of radius 1800m. Find the maximum lift force exerted on the 90 kg pilot by the plane’s seat. How many G’s does the pilot pull when he is in this position?

A 1200 kg car travels at 25 m/s over a woop-de-doo of dip radius 30 m and bump radius 50 m. Find the maximum constant speed (before contact with the road is lost) and the maximum normal force on the road that accompanies this constant speed.

Answers:

1) 1.5 sec; .003N, .1

2) 1.088N

3) 1.693N; 44.316 cm; 4.963 m/s; 5.61 sec

4) .638

5) 112 m

6) 111 g

7) 1.715 m/s

8) 6.261 m/s

9) 4.427 m/s

10) 5,382 N; 6.1

11) 31,360 N

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