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UNIT
4: DYNAMICS II
4.1 Circular Motion
(12 Periods)
 Speed of a body,
v = rw, moving with uniform angular speed
in a circle of radius r.
Centripetal acceleration,
a = v2 = rw2 and centripetal
force.
r
Examples
- Conical pendulum
- Banking of a road
- Upsetting and skidding
Translation and
rotation kinetic energy.
Assessment Objectives
By the end of this topic, the student should be able to:
- Define centripetal force.
- Define the radian.
- Derive and use the expression v = rw.
- Derive and use the expression a = v2/r
= rw2 and state its direction.
- Use the expression F = mrw2 = mv2/r
for centripetal force.
- Explain the following as applied to circular motion:
- conical pendulum
- banking of a road
- motion in a vertical circle.
- Describe conditions for skidding and toppling of
a cyclist or a vehicle
moving round a bend.
- Define moment of inertia about a given axis.
- State the expression for rotational K.E of a body
rotating about an axis with a
constant angular velocity.
- Distinguish between transitional and rotational K.E
- Relate work done by a couple to rotational K.E
4.2 Gravitation
(18 Periods)
Kepler's law's.
Newton's law's
of gravitation.
Gravitational field
including local variations of g.
Principle
of laboratory determination of G.
Gravitational Potential
Satellites
- Mechanical energy in a given orbit.
- Parking satellites.
Assessment Objectives
By the end of this topic, the student should be able to:
- State Kepler's laws
- State Newton's law of Gravitation.
- Derive dimensions of the gravitation G.
- Derive and use the relation between G and
g.
- Describe the principle of laboratory determination
of G.
- Derive and use Kepler's third law
T2 a r 3.
- Define and use gravitational potential.
- Define the velocity of escape ve
- Derive and use the expression ve =
ÖReg
- Describe the variation of g from
the centre of the earth to a point
above the earth's surface.
- Derive and use the formulae for K.E, P.E and mechanical
energy of
a satellite in orbit.
- Define parking orbit and relate it to communication
satellites.
- Derive and use the expression T2= 4pR3
for parking orbit./
Gr2
- Explain a state of weightlessness.
- Define free fall.
- Perform and describe an experiment to determine the
acceleration
of free fall.
4.3
Oscillations
(18 Periods)
4.3.1
Simple Harmonic Motion (SHM)
A special
periodic motion defined by a = -w2x.
Derivation
of the equation a = -w2x.
- a mass on a helical spring.
- a simple pendulum.
- a floating cylinder.
- a liquid in a U-tube.
Solution
of a = -w2x of the form x = A sin
wt or x = Acos wt
Graphical
representations of displacement, speed and acceleration
in SHM.
Phase difference
demostrated with two oscillating pendula or two masses
oscillating at the end of
helical springs.
Amplitude,
Period and frequency.
speed v = ± wÖ( A2 - x2
)
Interchange
of kinetic and potential energy in SHM.
Conservation
of Energy.
Measurement
of acceleration due to gravity using
- a simple pendulum.
- a mass of a helical spring.
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