Further Mechanics
- Created by: Sagaana
- Created on: 18-11-19 21:32
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- Further Mechanics
- Circular Motion
- Angular speed is the angle an object rotates per second
- you can link linear speed with angular speed using this equation
- Circular Motion has a frequency the number revolution per second. Unit: Hertz
- Frequency and time can be linked with this equation:
- Circular motion also has time period which is the time taken to complete a revolution
- Frequency and time can be linked with this equation:
- Circular motion also has time period which is the time taken to complete a revolution
- objects travelling in a circle are accelerating since their velocity is constantly changing ?
- Even though the car may travel at constant speed, its velocity is changing as the direction that it is travelling is constantly changing
- We define acceleration as a rate of change of velocity so the car is accelerating despite traveling at constant speed
- This acceleration is known as the centripetal acceleration.
- Centripetal force causes Centripetal Acceleration
- Using Newtons Second law, you can derive the equations for centripetal force
- It is what keeps the object moving is a circle or else it will just fly off.
- Simple Harmonic Motion
- What is simple harmonic motion?
- Features of SHM
- object with shm ocillates to and fro either side of the midpoint
- there is a restoring force pulling object to midpoint
- distance from midpoint= displacement
- An oscillation in which the accelaration is directly proportional to its displacement from the midpoint abs directed towards the midpoint
- object with shm ocillates to and fro either side of the midpoint
- Energy in mass- spring system
- towards midpoint restoring force does work so EPE -> KE and opposite when away from midpoint
- at midpoint EPE = 0 and KE = max
- Energy in Pendulums
- towards midpoint restoring force does work so GPE -> KE and opposite when away from midpoint
- at midpoint GPE = 0 and KE = max
- Total energy conserved
- Energy in mass- spring system
- towards midpoint restoring force does work so EPE -> KE and opposite when away from midpoint
- at midpoint EPE = 0 and KE = max
- Energy in mass- spring system
- The frequency and period are independent from amplitude for a pendulum
- The SHM equations
- acceleration is in the opposite direction
- velocity can cat in both directions so it is both positve and negative
- Displacement depends on time so when using this equation when t=0 x=A
- Features of SHM
- Simple Harmonic Oscillators
- Mass Spring System
- when mass is pushed around a force is exerted on the spring
- when you apply newtons second law you get the equation for the time period for a mass spring system
- Factors that affect the time period
- increase mass and time period increases
- spring constant increases the time period increases
- Amplitude has no affect on time period
- Mass are attached the ends of a spring
- Simple Pendulum
- blob attached to string which has no extension
- weight is perpendicular to string so restoring force is
- factors that effect the time period
- increasing length increases the time period
- changing mass has no effect on time period
- Amplitude has no effect on time period
- Mass Spring System
- Free and Forced Vibrations
- Free Vibrations
- oscillates at resonant frequency
- no energy transfered to surroundings
- this doesnt happen in practice
- Spring vibrating in air also called free vibrations
- Forced Vibrations
- when system forced to vibrate by an external periodic force
- the frequency of the external force = Driving Frequency
- Resonance when driving frequency = Resonant frequency
- Damping
- when system loses energy to the surroundings due to frictional forces..
- frictional force= damping force
- systems damped to reduce the effects of resonance
- Heavy Damping
- flatter resonance peak so not sensitive to driving force
- Critical Damping
- Light Damping
- sharp resonance peak
- OverDamping
- when system loses energy to the surroundings due to frictional forces..
- Free Vibrations
- What is simple harmonic motion?
- Circular Motion
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