Shm circular motion[1]

Name of student: ________________ sign of student: ____________

CIRCULAR MOTION……………..
YOU SHOULD KNOW:
1. For steady circular motion
i. v = rω
ii. T = 2π/ω
iii. f = 1/T
iv. f = ω/ 2π (w in rad s-1, 2π rad = 3600)
2. Acceleration in circle
i. a = v2/r
ii. a = rω2
(v changes in direction but not in magnitude, so steady speed)
3. Centripetal force F = mv2/r or F = mrω2
(F always acts towards the centre of the circle)
4. Conical pendulum resolve tension horizontally ( = mv2 / r ) or vertically ( = mg).

It is usual in circular motion to measure θ not in degrees, but also in radians (rad).
1 radian = 57.30
2π radians = 3600
 10 = π/180 rad
 1 rad = 180/π
(You will only be considering objects moving at a steady speed in a circular fashion. A change
in speed changes the radius of motion, which can force you to have to get messy with math.
We are considering cars on tracks, weights twirled on string, etc)

Imran Mirza (O & A Levels Physics Teacher) PGCC, Scotland, UK

bss.imranmirza65@yahoo.com (03336515500)


SIMPLE HARMONIC MOTION……………..

YOU SHOULD KNOW:
1. Definition of Simple Harmonic Motion (s.h.m.) is
a = -ω2x
(the minus sign is necessary because “a” is always directed towards a fixed point when at a
distance “x” from the centre of oscillation)
2. T = 2π/ω………., ω = 2πf
3. velocity v = ± √ω2(r2 – x2)..r = amplitude of the oscillation
4. vmax = ± ωr at x = 0 ( centre),
5. v = 0 at x = r (rad)
6. amax = -ω2r at x = r (rad)…
7. a = 0 at x = 0 (centre)
8. Kinetic energy = max ( 1/2mr2ω2 ) at x = 0 (centre)
9. Kinetic energy = 0 at x = ±r (end)
10. Potential energy = max ( 1/2mr2ω2 ) at x = ±r (end)
11. Potential energy = 0 at x = 0 (centre)
12. Total Kinetic energy and Potential energy = constant




SIMPLE HARMONIC MOTION……………..

(Simple pendulum)

1. T = 2π √l/g provided very small angle of oscillation and very small mass

(Spring – Mass System)
You should know………..
1. Spring and mass on smooth horizontal table,
T = 2π √m/k (F = -k x for spring)
2. Mass suspended from vertical spring,
T = 2π √m/k = √e/g (where mg = ke)
(Formula can be applied to vibrations of ions in crystals, to radio circuits and to mechanical
vibrations)
3. Oscillations in mass-spring system are due to continuous exchange of energy.
4. For spring potential energy = ½ kx2
5. for mass kinetic energy = ½ mv2, and total energy stays constant

RESONANCE

1. At resonance,
External frequency = natural frequency, amplitude large




CIRCULAR MOTION

Assignment No: __ A-LEVEL Dated:________

Q1: Express the following in π radians
1: 1200
2: 2400
3: 900
centripetal acceleration……….
Q2: the blades on a propeller make 50 revolutions per second. The diameter of the circle the
blades describe is 4 m. Find
a. the angular speed ω
b. the linear speed of the tip of the blade
c. the centripetal acceleration of the tip of the blade
d. how would the acceleration vary from the centre of the blades to the tip?

Do not try to use a = v2 / r to answer (d) as v is no constant.

centripetal force………
Q3: A conker of mass 0.05 kg is twirled on a string vertically at a constant speed. Its circular
path is of radius 60 cm and its angular speed is 15 rad s-1
a. find the tension in the string in the “3” positions shown
A

O B

C
b. why is the string more likely to break in position C?

(Keeping the angular speed constant is actually impossible, but don‟t let that stop you enjoying
yourself answering this lovely question)
Remember that the centripetal force is result of other forces acting




CIRCULAR MOTION


Q1: (a). What is meant by „centripetal force‟?
(b). What is „centrifugal force‟?
(c). In what direction does a centripetal force act?
(d). What is „angular velocity‟?
(e). Why are centripetal forces not put in free-body force diagram?
Q2: A car of mass 800 kg is turning a corner with a radius of curvature of 25 m. where does
the centripetal force come from, and what is the maximum speed it can take through this
corner if the centripetal force is 3000 N?
Q3: A toy car does a „loop-the-loop‟ (below) . what is its maximum velocity if it just remains
in contact with the track at the top of the circle, if the circle has a radius 0.50 m? if the car
starts from rest at a point A, what would be the height of point A above the ground?
A

h

Q4: A child is sitting on a fairground. The ride turns through one complete revolution every
four seconds. If the combined mass of the child and the seat is 40 kg, and the radius of the
circular path is 6.0 m, calculate the tension, T, in the support.

T

6.0 m 40 kg




CIRCULAR MOTION


Q1: A van is going round a corner with a banked track, as shown in fig. if friction is
negligible where does the centripetal force come from, and what is the angle of banking
required if the speed is 14 m/s and the radius of curvature is 30 m?
R

W

Q2: The blades of a helicopter droop as shown in fig. The maximum angular velocity the can
rotate at with this droop before breaking is 5.0 rev/s. if the length of the blades is 5.0 m,
and their mass is 30 kg, what force is needed to break the blades?

200




SIMPLE HARMONIC MOTION… (SHM)

Q1: some ripples on water travel at 0.15 ms-1, have a wavelength of 30 mm and amplitude of
10 mm. What is the maximum velocity of a point on the water surface?

Q2: A Malteser rolls in a smooth bowl with SHM of amplitude 30 mm. its mass is 10 g and
the maximum force acting on it 0.05 N
Find
a. its maximum velocity
b. its period of oscillation

The clue to the SHM equations is often to find ω, and then use it
in the other equations to find you need





Q1: (a). define „SHM‟.

(b). where is the acceleration greatest in an „SHM‟ oscillation?

(c). Where is the velocity greatest in an SHM oscillation?

(d). What is meant by the „natural frequency‟ of an oscillation?

(e). When does resonance occur?

(f). Where is the potential energy greatest in an SHM oscillation?

(g). Where is the kinetic energy greatest in an SHM oscillation?

(h). What two properties are required to perform SHM?

(i). What is the most useful application of SHM oscillation?

(j). What is meant by critical damping?





Take g = 9.8ms-2
Q1: An object is oscillating from side to side, performing SHM. The time period is 2.0 s, and
the amplitude is 3.0cm. What are the maximum velocity and acceleration, and the
acceleration 1.0 cm from the centre?

Q2: A pendulum of length 2.0 m is swinging between two points 40 cm apart. What is the
time period of oscillation and the maximum KE of the pendulum if the mass of the
pendulum bob is 200 g?

Q3: An oscillating spring system as shown in fig



Shm circular motion[1]

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