LEARNING OBJECTIVES

Knowledge & Understanding

- Distinguish between rectilinear and curvilinear motion.
- Define the terms: projectile, trajectory, elevation angle, impact angle, ballistics.
- Describe the forces acting on projectiles and calculate the time of flight, range, impact velocity and maximum height of a projectile.
- Explain circular motion in terms of an unbalanced centripetal force.
- Discuss the motion of objects travelling in circular paths.
- Solve problems involving objects moving in circular paths (a
_{c}= v^{2}/r = 4p^{2}r/T^{2}). - Distinguish between angular and tangential velocity and solve problems involving radial motion.
- Explain what simple harmonic motion (SHM) is and define the conditions for its existence.
- Explain the terms: amplitude, oscillation, period, frequency, restoring force, spring constant.
- Give examples of everyday objects moving under simple harmonic motion.
- Calculate the maximum velocity, acceleration and forces acting in SHM.
- Describe the motion of a swinging pendulum and a vibrating mass attached to a spring.
- Relate SHM to uniform circular motion.

Scientific Techniques

- Plot and analyse graphically, data relating to mass, velocity, radius and centripetal forces acting on objects swung in horizontal circles.
- Compare vertical and projectile motion in the laboratory.
- Observe and tabulate data related to an oscillating spring and a simple pendulum.

Complex Reasoning

- Solve problems combining circular, linear and projectile motions.
- Predict motion of projectiles in cases where friction is significant.
- Solve problems relating to loop-the-loop motion.

- For a projectile, the vertical and horizontal motions are independent.
- The angle at which the object is thrown relative to the horizontal is called the elevation angle.
- The motion of the projectile is a parabola because the vertical displacement varies as a function of t
^{2}. - The impact velocity will have the same magnitude as the launch velocity, but be directed down not up.
- The horizontal displacement is called the range.
- The range of a projectile will be the same for elevation angles of θ and 90-θ. These are called complementary angles.
- The maximum range can be calculated by letting θ = 45°.
- Air resistance affects the trajectory of a projectile by reducing its range, lowering its maximum height and making the flight path non-symmetrical.
- The centripetal force is the net force directed towards the centre of a circular path.
- An object travelling in a circle at constant speed has an acceleration called centripetal acceleration, directed towards the centre of the circular path.

a_{c}= v^{2}/r. - The centripetal force is the net force directed towards the centre of a circular path.

F_{c}= m v^{2}/r. - When a car travels around a bend in a road, the maximum safe speed for the car is given by:

v_{max}= √(µgr). - For motion in a circle: v = s/t = 2 p r /T
- For circular motion in a vertical circle:

Forces at top of circle: F_{c}= mv^{2}/r = T + F_{w}or T = F_{c}- F_{w}

Forces at side of circle: F_{c}= mv^{2}/r = T

Forces at bottom of circle: F_{c}= mv^{2}/r = T - F_{w}or T = F_{c}+ F_{w}

- Minimum speed to stay in orbit at top of vertical circle:

v_{min}= Ögr or (gr)^{½}.

- Maximum force or tension is at bottom of vertical circle.

T = F_{c}+ F_{w} - Acceleration is often expressed in multiples of 'g' (10 m s
^{-2}). - There are 2p radians in a circle of 360° this equals one revolution.
- One revolution per second (rps) = 2 p rad s
^{-1}; 'rpm' stands for revolutions per minute. - Angular motion formula: v = w r or w = v/r

a_{c}= v²/r = w²/r = w v and F_{c}= mv²/r = m w²/r

- Periodic motion is motion in which an object continually moves back and forth over the same path in equal time intervals. A mass hanging on a spring and a pendulum are examples of this.
- Simple harmonic motion (SHM) is periodic motion in which the restoring force is proportional to the displacement from equilibrium but in the opposite direction:

F proportional to -x or F = - k x

- The constant (k) is called the spring constant. Its units are N m
^{-1}. - The period (T) of SHM is given by T = 2 p (m/k)
^{½} - The time for one oscillation is the period (T). The number of oscillations per second is called its frequency (f). The sideways displacement (x) is the sideways distance from the vertical or equilibrium position. The maximum displacement during the oscillations is called the amplitude.
- The period of a pendulum is given by T = 2 p(m/k)
^{½} - Simple harmonic motion is the projection of uniform circular motion on the diameter of the circle in which the circular motion occurs.

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