uniform circular motion i. depicting circular motion a...
TRANSCRIPT
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
UNIFORM CIRCULAR MOTION
Why are there 6.28 radians in a circle?
It is not random….
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
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UNIFORM CIRCULAR MOTION
If
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
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
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 CONSIDER: An object moving in a
circle, radius R, at constant speed v.
Source: Physics for the IB Diploma, 5th Ed, Tsokos
UNIFORM CIRCULAR MOTION
VECTOR DIAGRAMS OF CIRCULAR
MOTION
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
Source: Physics for the IB Diploma, 5th Ed, Tsokos
UNIFORM CIRCULAR MOTION 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
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
Source: Physics for the IB Diploma, 5th Ed, Tsokos
UNIFORM CIRCULAR MOTION 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
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.
UNIFORM CIRCULAR MOTION 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
ACCELERATION TOWARDS THE
CENTER OF A CIRCLE
REMEMBER: v tangent to the circle, Δv always points inwards (also a)
Source: Physics for the IB Diploma, 5th Ed, Tsokos
UNIFORM CIRCULAR MOTION 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
UNIFORM CIRCULAR MOTION 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
EQUATING CENTRIPETAL FORCE
TO OTHER FORCES
Source: Physics for the IB Diploma, 5th Ed, Tsokos
UNIFORM CIRCULAR MOTION 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
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.
UNIFORM CIRCULAR MOTION 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
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.
UNIFORM CIRCULAR MOTION 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
Source: IB Past Papers
UNIFORM CIRCULAR MOTION 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
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.
UNIFORM CIRCULAR MOTION 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
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.
UNIFORM CIRCULAR MOTION 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
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?