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To make an object move in a circle with a constant speed, a force must act on it that is directed where?
-towards the center of the circle
In circular motion, does direction change frequently?
-yes, direction changes continuously
What is produced whenever the direction of a velocity changes?
-acceleration
In what direction does this acceleration act?
-towards the center of the circle
What is this center-directed acceleration called?
-centripetal acceleration
What is the magnitude of centripetal acceleration equal to? (in equation form)
acceleration centripetal = v^2/r
What must be applied to an object to give it a circular motion?
-centripetal force
For an object of mass m, what is the magnitude of the net force acting on it? (in equation form)
force centripetal = m(v^2/r)
How can centripetal force be produced?
-in any number of ways
What are some examples of how centripetal force may be produced?
-might be the tension in a string
-might be due to friction between tires and the road
-could be the force of gravity causing a satellite (or the Moon) to orbit the earth
If we are studying a system where the force of static friction provides the centripetal force required to move a car in a circular path, what is the effect of decreasing the radius the car's path?
-maximum speed that the car can have in a corner with out skidding decreases
The effect of reducing the coefficient of static friction?
-again, the maximum speed that the car can have in a corner with out skidding decreases
The effect of reducing gravity (if for instance the car was transported to the moon)?
-again, the maximum speed that the car can have in a corner with out skidding decreases
Of reducing the car's weight?
-no effect whatsoever, as mass is irrelevant
If you experience skidding while rounding a corner too rapidly, what should you do?
-turn in the direction of the skid to regain control
Why?
-if you turn in the direction of the skid, you increase your turning radius
What is the effect on centripetal acceleration?
-centripetal acceleration decreases
Why are many roads tilted/banked when they round a corner?
-the banking tilts an automobile in toward the center of the circular path it is following
-on a banked curve, the normal force exerted by the road contributes to the required centripetal force
-if the tilt angle is just right, the normal force provides all of the centripetal force so that the car can negotiate the curve even if there is no friction between its tires and the road
Given a person in a car that encounters a dip in the road. Does the person feel heavier or lighter than when on a flat road?
-heavier
Why?
-at the bottom of the dip, the normal force is greater than the weight of the passenger, since it must also supply the centripetal force (N = centripetal force + mg)
Given a person in a car that encounters a bump in the road. Does the person feel heavier or lighter?
-lighter
Why?
-at the top of the bump, the normal force is less than the weight of the passenger (N = mg - centripetal force)
Can an object moving in a circular path increase or decrease its speed?
-yes
-to be fully explored later
In order for velocity to be constant, what conditions must be met?
-velocity must have constant speed AND direction
Describe the direction of an object that moves in a circle at constant speed
-direction is constantly changing
Is the velocity of the object constant?
-no
Why not?
-because direction is constantly changing
What then do we know about the force acting on an object moving in a circle?
-force must be greater than zero
If net force is zero, can an object remain in a circle?
-no
What would happen to the object if net force is zero?
-the object would travel in a straight path
What must be done to keep an object on a circular path?
-it must be continually be nudged
In was direction does Fnet point when an object is in uniform circular motion?
-towards the center of the circle
What does the object never have the opportunity to do?
-follow its own inertia
What two forces can act on objects in circular motion?
-tangential force and centripetal force
In what direction does tangential force operate?
-parallel to velocity
If the tangential force is parallel to velocity, what effect does it have on an object?
-it causes the object to accelerate, thereby changing velocity
As a result, what does Ilka refer to tangential force as?
-"speed control"
In what direction does centripetal force operate?
-perpendicularly to velocity
-radially inward
If the centripetal force is perpendicular to velocity, what effect does it have on an object?
-nudges an object to change direction
As a result, what does Ilka refer to centripetal force as?
-"direction control"
What effect does tangential force have direction?
-no effect
What effect does centripetal force have on speed?
-no effect
When velocity changes, what force is responsible?
-acceleration
In what direction does centripetal force operate?
-radially inward
-pulls objects toward the center of a circle
What is the size of centripetal force equal to? (equation)
Centripetal force = m*v^2/r
What is the size of acceleration due to centripetal force equal to?
Centripetal acceleration = v^2/r
Is centripetal force a force in and of itself?
-no
If not, what is it?
-centripetal force is a condition that must be met
-a label for the requirement of force that must be provided for successful circular motion
What can help to meet the requirement?
-requirement can be met by one or more of the following: force of gravity, normal force, tension force, force of friction
If the energy required for circular motion is greater than actual energy, what will be the path of an object?
-the object will fly out of the circle
If the energy required for circular motion is less than actual energy, what will be the path of an object?
-the object will move closer and closer towards the center of a circle
What will occur when the energy required for circular motion equals actual energy?
-the object will move in a circle
What will be the distance the object from the center of the circle over time?
-the object will maintain the same distance from the center of the circle
What is the value for centripetal force dependent upon?
-mass
-speed
-radius of circle
If you want to achieve a low centripetal force, what relative mass, speed, and radius do you want?
-low mass
-slow speed
-large radius
And if you want to achieve a high centripetal force?
-large mass
-fast speed
-tight radius
What is centrifugal force often described as?
-while you are turning when riding in a car, it feels as if there is an outward pull on those in a car
Does this force exist?
-no, it is not real
How does it feel if you take a right turn?
-it feels as though you are being thrown outward against the left door
Are you being thrown outward against the left door?
-no, you are not
Then why does it feel as if you are?
-your body has inertia, and it wants to continue to travel forward (instead of right)
-the car door refuses to let you do so, and holds you in
What would happen if you opened the car door during the right turn?
-you would fall out of the car in a straight line
If a car is moving over a bump on a road while moving at constant velocity, what forces act on it?
-normal force and force of gravity
If there is no net force on the vehicle, in what direction would it move at the top of the bump?
-in a straight line
As such, is there a net force on the vehicle as it moves over the bump?
-yes
What is this force called?
-centripetal force
In what direction does the force act in?
-downward, towards the middle of the circle (formed by the bump)
What force then provides the centripetal motion?
-the force of gravity
What is normal force equal to in this instance?
normal force = mg - mv^2/r
Is the normal force equal to or lesser than the force of gravity?
-less than the force of gravity
What will the apparent weight of the driver of the car be as the car passes over the bump?
-apparent weight will be less than actual weight
If a scale was in the car, what would the reading be?
-less than actual weight
What elevator ride situation is this similar to?
-similar to downward acceleration in an elevator
In both cases, in order for Fnet to be downward, what force must win?
-gravity
What is the only difference between the described movement in the car and the elevator motion?
-sideways motion: when traveling over a bump, you are experiencing acceleration towards a point that you will never reach, due to sideways motion
If at the top of the bump, you continued on in a straight line, what would you be doing in terms of circular motion?
-you would be flying out of the circle
In that instance, what is the relationship between required force and actual force?
-required force is greater than actual force
When driving over a bump, what occurs when actual force is greater than the required force?
-nothing
Why not?
-because the road prevents the car from moving towards the center of the circle
When a bucket on a string is tethered to fixed point, compare the speed of the bucket at the top of its motion to the speed of the bucket at the bottom of its motion
-speed of the bucket is greater at the bottom of the motion
Why?
-because the force of gravity will have a component that reinforces the direction of motion
At the bottom of the bucket's motion, which forces act on the bucket?
-tension and force of gravity
What is the relationship between tension and the force of gravity?
T > mg
-->act antagonistically
Why?
-the "up" force of tension must beat the "down" force of gravity for the bucket to maintain circular motion
What if T = mg?
-then the bucket would move in a straight line because it experiences no net force
At the top of the bucket's motion, what forces act on the bucket?
-tension force and gravity
What is the relationship between tension and the force of gravity? Do they act antagonistically?
-no, they do not act antagonistically
As a team, what do they provide?
-the centripetal force required to keep the bucket in a circular motion
What does tension provide?
-whatever force that gravity cannot contribute
How do you calculate the minimum speed necessary to maintain circular motion at the top of the movement?
v = SQRT(rg)
A car is driven with constant speed around a circular track. Is its velocity constant?
-no, velocity is not constant because the direction in which the car moves is changing
Is the magnitude of its acceleration constant?
-the magnitude of the car's acceleration is given by the equation v^2/r
-->since the speed and radius are constant, so is the magnitude of the acceleration
Is the direction of its acceleration constant?
-the direction of the car's acceleration is toward the center of the circular path
-->thus, the direction of the acceleration changes as the car moves around the circle
Water sprays off a rapidly turning bicycle wheel. Why?
-for a drop of water to stay on a rotating wheel, an inward force is required to give the drop the necessary centripetal acceleration
-->since the force between a drop of water and the wheel is small, the drop will separate from the wheel rather than follow its circular path
In a circus act, a motorcyclist drives his bike around the inside of a vertical circle. How is this possible?
-a centripetal force is required to make the motorcycle follow a circular path
-force increases rapidly with speed
-->if the necessary centripetal force exceeds the weight of the motorcycle (because its speed is high enough), then the track must exert a downward force on the cycle at the top oc the circle
-->this keeps the cycle in firm contact with the track
A popular carnival ride has passengers stand with their backs against the inside wall of a cylinder. As the cylinder begins to spin, the passengers feel as if they are being pushed against the wall. Explain.
-since the passengers are moving in a circular path, a centripetal force must be exerted on them
-->this force, which is radially inward, is supplied by the wall of the cylinder
The gas pedal and the brake pedal are capable of causing a car to accelerate. Can the steering wheel also produce an acceleration? Explain.
-yes, the steering wheel can accelerate the car by decreasing the radius of the turn
When rounding the corder on a bicycle or a motorcycle, the driver leans inward, toward the center of the circle. Why?
-when a bicycle rider leans inward on a turn, the force applied to the wheels of the bicycle by the ground is both upward and inward
-it is this inward force that produces the centripetal acceleration of the rider
