Futher Mecahnics Flashcards
What kind of force is required to keep and object moving in a circle at constant speed
A constant Centripetal force
(a force that is always applied towards the centre of the circle)
Describe the motion of an object traveling at a constant speed within a circle.
1) Accelerating towards a fixed point in the centre,as the direction is always changing, hence the velocity is always changing so the object is accelerating.
2) Angular & linear speed is constant (Radians per second & meters per second )
How do you calculate angular speed (omega)
Omega = Velocity/radius
Omega = 2pifrequency
Omega = (2*pi)/Time period
How do you calculate angular acceleration? (2 ways)
A = Omega^2 * radius
A = Velocity^2 / Radius
What is the formula for centripetal force
F = mA
F = m * velocity^2 / radius
F = m * Omega^2 * radius
What are the conditions for SHM
. Acceleration must be proportional to its displacement from the equilibrium point
. Acceleration is always acting in the opposite direction to displacement
What is displacement as a trig function of time and angular speed
Displacement = Amplitude * cosine( Omega * time)
How do you calculate speed using Angular velocity and Amplitude
Derivative of Amplitude* cosine(omega * time)
Velocity = omega * Amplitude* sine(omega * time)
Note can be cos too depending what you use.
Ho do you calculate maximum speed? (SHM)
Omega*Amplitude
Omega = Angular speed
as cos(wt) = 1
How do you calculate acceleration using angular velocity and amplitude
Derivative of Amplitude* cosine(omega * time) in respect to time
Velocity = (omega)Amplitude sine(omega * time)
Acceleration = Derivative of velocity in respect to time
Acceleration = -1* (omega)^2 * Amplitude * cosine(omega * time)
Note can be cos too depending what you use.
How do you calculate maximum acceleration in shm
Omega^2 * Amplitude
How would you calculate the time period for a mass spring system undertaking in simple harmonic motion
How would you calculate the time period for a simple pendulum undertaking in simple harmonic motion
Draw the graph for the potential energy and kinetic energy against displacement for a SHM system.
Define Free vibrations
oscillations where’re there are no damping frictional forces and the amplitude is constant