Horizontal Circular Motion

Horizontal Circular Motion

ReviewReviewIf an object travels at a constant velocity

a = 0

Fnet = 0

If an object travels with a changing velocity

.

.

What if?What if?What if you do not speed up or slow down, but change direction?

Velocity changes (vector)

Acceleration occurs

Fnet

Centripetal AccelerationCentripetal

AccelerationCentripetal - center seeking

points towards the center of the circle

sometimes called radial acceleration

dependent on v and r

ExampleExampleA ball at the end of string is revolving in a horizontal circle of radius 0.6 m. The ball makes 2 revolutions in a second. What is the centripetal acceleration?

ExampleExampleA jet plane traveling at 525 m/sec pulls out of a dive by moving in an arc of radius 6 km. What is the plane’s centripetal acceleration?

Dynamics of Circular Motion

Dynamics of Circular Motion

If there is an acceleration, Newton’s Second Law requires a net external force

Since the acceleration is centripetal, the net force must also be centripetal

Centripetal ForceCentripetal ForceBut that would mean centripetal force is not a real force, but is a net force and caused by something else.

Fw, Fn, Ft, Ff

Okay, that other ForceOkay, that other ForceCentrifugal - an outward force acting on an object moving in a circular path

Everyone has felt it

So, what do you feel? Depends on who “you” are.

Centrifugal ForceCentrifugal ForceIf there was a centrifugal force acting on the ball, what would happen if you let it go?

Sample ProblemSample ProblemSample ProblemSample Problem

A 10 kg mass is A 10 kg mass is attached to a string attached to a string that has a breaking that has a breaking strength of 200 N. If strength of 200 N. If the mass is whirled in the mass is whirled in a horizontal circle of a horizontal circle of radius 0.8 m, what radius 0.8 m, what maximum speed can maximum speed can it have?it have?

Circular Circular MotionMotion

A ReviewA Review

Circular Circular MotionMotion

A ReviewA ReviewIn most cases, the In most cases, the string force not string force not only has to provide only has to provide the force required the force required for circular motion, for circular motion, but also the force but also the force required to balance required to balance the gravitational the gravitational force.force.

DynamicsDynamicsSince there is a net force, we need to know which forces are acting ON the object and then solve.

A 300 g tetherball is attached to a massless rope 2 m long. If the rope makes an angle of 30o to the vertical, what is the speed of the ball?

Sample ProblemSample ProblemSample ProblemSample Problem

In a version of a “Giant In a version of a “Giant Swing”, the seat is Swing”, the seat is connected to two cables as connected to two cables as shown. The seat swings in shown. The seat swings in a horizontal circle at a rate a horizontal circle at a rate of 32 rpm. If the seat of 32 rpm. If the seat weighs 255 N and a 825 N weighs 255 N and a 825 N person is sitting in it, find person is sitting in it, find the tension in each cable.the tension in each cable.

Circular Motion and Circular Motion and FrictionFriction

Circular Motion and Circular Motion and FrictionFriction

This required force is This required force is provided by the friction provided by the friction force between the tires force between the tires and the road.and the road.

But remember ….. The But remember ….. The friction force has a friction force has a maximum value, and maximum value, and there is a maximum there is a maximum speed with which you speed with which you can make the turn.can make the turn.

Highway CurvesHighway CurvesA 1000 kg car rounds a curve on a flat road of radius 50 m at a speed of 15 m/sec. What minimum coefficient of friction is needed for the car to safely navigate the corner?

SampleSampleA flat puck of mass M is rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block of mass m. What is the speed of the flat puck if the radius of the circle is R?

samplesampleA 4 kg object is attached to a vertical rod by two strings. The object rotates in a horizontal circle at constant speed 6 m/sec. Find the tension in each of the strings.

Vertical Circles

Vertical CirclesMotion in a vertical circle is no different, other than the weight of the object now comes into play.

Look at the forces acting on the passenger to keep them in the circular path both at the top and the bottom.

Ferris WheelA passenger on a Ferris wheel moves in circle of radius 8 m. The passenger’s mass is 60 kg and the wheel completes one revolution in 10 sec at a constant speed. What is the normal force of the seat on the passenger both at the top and the bottom?

ExampleA bowling ball weighing 70 N is attached to a ceiling by a 4 m long rope. The ball is pulled back until the rope makes an angle of 30o to the vertical. The ball is then released. Determine:

the speed of the ball when the rope is vertical.

the tension in the rope when the rope is vertical.

amusement Park PhysicsWhat is the minimum speed that a roller coaster must be traveling when upside down at the top of a circle so that the passengers do not fall out? Assume a radius of 7.4 m.

amusement Park PhysicsIf the riders are at the top with the speed you just found, how fast will they be moving when they get to the bottom?

What will the normal force be on the passengers at the bottom assuming they are still moving in a circular path?

Amusement park physics

A roller-coaster car has a mass of 500 kg when fully loaded with passengers.

what is the maximum speed the vehicle can have at B and still remain on the track?

with that speed at b, what is the normal force of the track on the car at point A?