Uniform Circular Motion

Ms Mikaela Fudolig

Physics 71 EEE Lecture

Uniform Circular Motion

Object moves at constant speed in a circleIs its velocity constant?

Centripetal Acceleration

Inward central acceleration

Centripetal Force

Inward central net forcecentripetal force is not a kind of force (e.g.,

weight, tension, etc)

Centripetal vs Centrifugal

If the force acting on an object moving in uniform circular motion points inward, why do we feel an outward force when we move in a circle?Non-inertial reference frame

Velocity

Velocity is always tangent to the circle

Conceptual Exercise 1

A boy whirls a stone of mass m at the end of a string L so that it moves in a circle with constant speed. If the string were suddenly cut, in what direction will the stone move?

Conceptual Exercise 2

What is the direction of the (a) acceleration and (b) velocity of a Ferris wheel car atits highest point?its lowest point?

Conceptual Exercise 3

Why is it that objects in uniform circular motion don’t crash even if their acceleration is inward?

Period, TTime it takes for object to complete one

cycle.

Speed

total distance

total timeavv v

2 rv

T

r=radius of circle

T=period

v=speed

Exercise 2

If Olop, the other reindeer, Santa and the sleigh were undergoing circular motion at a constant speed of 10m/s, and if it took them 1 hour to come back to where they were initially, how far did they travel?

2 rv

T

r=radius of circle

T=period

v=speed

Exercise 3a

An object with mass m is observed to have a period T when undergoing circular motion at a constant speed v. The total distance traveled is 2r.If the mass is increased to 2m, how long will it

take the object to undergo circular motion and travel a distance 2r at constant speed v?

Exercise 3b

An object with mass m is observed to have a period T when undergoing circular motion at a constant speed v. The total distance traveled is 2r.If the speed is increased to 2v, how long will it

take the object to undergo circular motion and travel a distance 2r?

Ans: ½ T

Centripetal Acceleration: Magnitude

The centripetal acceleration has a magnitude

2va

r v=speed

r=radius of circle

UNIFORM AND NON-UNIFORM CIRCULAR MOTION (for non-uniform circular motion,

this is just the perpendicular component of a)

Exercise 4

An athlete is jogging at a constant speed of 1m/s in a circular track 200m long. What is the magnitude of the athlete’s centripetal acceleration?

2va

r

v=speed

r=radius of circle

Centripetal Force: Magnitude

The centripetal force has a magnitude

2

net

mvF ma

r

v=speed

r=radius of circle

m=mass

Solving problems involving the centripetal forceDraw a free-body diagram of the object.Apply Newton’s 2nd Law.

Example 1

A sled with a mass of 25.0kg rests on a horizontal sheet of essentially frictionless ice. It is attached by a 5.00m rope to a post set in the ice. Once given a push, the sled revolves uniformly in a circle around the post. If the sled makes five complete revolutions every minute, find the tension in the cord.

Exercise 5: Conical Pendulum

A ball of mass m is suspended from a rope of length L and travels at constant speed in a horizontal circle of radius r. The rope makes an angle with the vertical. Find the:tension in the ropespeed of the ball

Cars on unbanked curves

A car is moving with constant speed on an unbanked circular track. What are the forces acting on the car?weightnormal forcefriction

static or kinetic?

Exercise 6: Unbanked curves

A race car was able to travel at constant speed v in a circle of radius 45.7m in 15.2s without skidding. Find the:average speedcentripetal accelerationMinimum possible value of s (i.e., assume that

friction has reached its maximum value for the car to move in this manner)

Banked curves

makes circular motion in frictionless surfaces possible.

forces acting on object:normal forceweight

Free-body diagrams: do NOT rotate axes

Exercise 7

A curve of radius 30m is banked at an angle . Find for which a car can round the curve at 10m/s even if the road is frictionless.

Uniform Circular Motion in a Vertical PlaneConstant speedAcceleration

constant magnitudepoints inward

Exercise 8a: Ferris wheel

A passenger on a carnival Ferris wheel moves in a vertical circle of radius R with constant speed v.Draw a free-body diagram for the passenger

when he is (a) at the top of the circle and (b) at the bottom.

Exercise 8b: Ferris wheel

A passenger on a carnival Ferris wheel moves in a vertical circle of radius R with constant speed v.Find the normal force exerted by the seat on

the passenger when he is (a) at the top of the circle and (b) at the bottom.