UNIFORM CIRCULAR MOTION I. DEPICTING CIRCULAR MOTION A ...mrsmithsphysics.weebly.com/.../2.4_uniform_circular_motion_class_notes.pdf · uniform circular motion i. depicting circular

UNIFORM CIRCULAR MOTION

MATHEMATICS OF CIRCLES AND

RADIANS

I. DEPICTING CIRCULAR MOTION

A. MATHEMATICS OF CIRCLES AND RADIANS

B. VECTOR DIAGRAMS OF CIRCULAR MOTION

II. CENTRIPETAL FORCE AND ACCELERATION

A. ACCELERATION TOWARDS THE CENTER OF A CIRCLE

B. EQUATING CENTRIPETAL FORCE TO OTHER FORCES


Why are there 6.28 radians in a circle?

It is not random….







s


If







Understand how the sine and cosine functions can be graphed along the

x axis, especially why the units of x-axis are radians.

Source: Calculus, Swokowski

UNIFORM CIRCULAR MOTION I. DEPICTING CIRCULAR MOTION





B. EQUATING CENTRIPETAL FORCE TO OTHER FORCES CONSIDER: An object moving in a

circle, radius R, at constant speed v.

Source: Physics for the IB Diploma, 5th Ed, Tsokos


VECTOR DIAGRAMS OF CIRCULAR

MOTION














EXAMPLE 1

A mass on a string moves in a circle of radius 3.0 m with a constant speed of v

= 6.0 ms-1. However, v changes constantly (why?) and is at all times tangent to

the circular path as shown. The mass goes from A to B to C. Find:

b) Δv (vC – vB) between B and C

a) Δv (vB - vA) between A and B








HWSP #1

Estimate the linear speed of an object at the equator due to the rotation of the

Earth. [470 ms-1]

EXAMPLE 2

Repeat HWSP #1 at 2 other locations:

a) 30° latitude b) 65° latitude.







ACCELERATION TOWARDS THE

CENTER OF A CIRCLE

REMEMBER: v tangent to the circle, Δv always points inwards (also a)














EQUATING CENTRIPETAL FORCE

TO OTHER FORCES








HWSP #3

A model airplane of mass 0.25 kg has a control wire of length 10.0 m attached

to it. While held in the hand of the controller, it flies in a horizontal circle with a

speed of 20.0 ms-1. Calculate the tension in the wire.







HWSP #4

A car is travelling at constant speed of 18 ms-1 around a horizontal bend in the

road. The mass of the car is 1.5 × 103 kg and the bend forms part of a circle of

radius 2.0 × 103 m. Determine the frictional force between the tyres of the car

and the surface of the road that produces the acceleration.

HWSP #7

A ball of mass 0.25 kg is attached to a string and is made to rotate with

constant speed v along a horizontal circle of radius r = 0.33 m. The string is attached to the ceiling and makes an angle of 30° with the vertical.

a) On the diagram, draw and label arrows to represent the forces on the ball in

the position shown.

b) State and explain whether the ball is in equilibrium.

c) Determine the speed of rotation of the ball.







Source: IB Past Papers







EXAMPLE 3

A particle of mass m is moving with constant speed v in uniform circular motion.

Determine the total work done by the centripetal force during one revolution in

terms of the appropriate variables.







EXAMPLE 5

A mass m is tied to a string and made to move in a vertical circle of radius R

with constant speed v. Find the tension in the string at the lowest and highest

points.







HWSP #5

A daredevil motorcyclist rides his motorcycle on a track that makes a vertical

circle of radius 20.0 m. What is the minimum speed that he must have at the

top of the circle in order to complete the loop?

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UNIFORM CIRCULAR MOTION I. DEPICTING CIRCULAR MOTION A ...mrsmithsphysics.weebly.com/.../2.4_uniform_circular_motion_class_notes.pdf · uniform circular motion i. depicting circular