Further Mechanics Flashcards
If an object is moving in circular motion at a constant speed what two things must there be?
acceleration
centripetal force
What 3 equations can be used to calculate the magnitude of angular speed?
ω = 2πf
ω = v/r
ω = Δθ/Δt
where θ is in radians
How do you convert degrees to radians?
θ x 2π/360 = angle in radians
Define angular velocity.
the rate of change of angular displacement
What is angular velocity measured in?
radians per second
What is angular displacement?
the angle moved through relative to a specific axis (the angle between the radius of the circle at the initial position and its final position)
How is time period, T, calculated?
total time taken / number of rotations
What is the velocity, v?
the velocity at which the object is moving around the circle, measured in m/s
How is velocity of an object travelling in circular motion calculated?
v = 2πr/T v = rω
Why does an object moving in circular motion have an acceleration even if it is moving with constant velocity?
the angular velocity is always changing as the tangent to the circle at which the body is moving is constantly changing. Even if it is at a constant speed, the direction in which it is moving is changing, meaning its angular velocity is changing. where there is a change in velocity there is acceleration
Define acceleration.
rate of change of velocity
What is the name given to acceleration due to circular motion?
centripetal acceleration
Why does the object have a centripetal force?
F=ma, the body has mass and centripetal acceleration and therefore has a centripetal force holding it in circular motion
In which direction does the centripetal force act?
towards the centre of the circle, perpendicular to the velocity.
Which factors affect the magnitude of centripetal force?
mass, velocity, radius
Which equations can be used to calculate centripetal acceleration?
a = v^2 / r a = ω^2 x r
Which equations can be used to calculate centripetal force?
F = mv^2 / r F = m x ω^2 x r
Which equation can be used to calculate the force on an object?
F - Fr = ma
What is an example of a centripetal force?
friction
gravity
tension
What is represented by μ in the equation Fr = R x μ
where Fr is the frictional force and R is the resultant force (often equal to mg)
the coefficient of friction between the object and the surface
How do you calculate the greatest speed a car can do without losing contact with the ground?
Friction = mv^2 / r Friction = μmg
so max v = the square root of μmg
What condition is necessary for simple harmonic motion to occur?
a ∝ -x
where a is the acceleration and x is the displacement
What equation can be used to calculate the acceleration of an object inn simple harmonic motion?
a = ω^2 x (x)
What is an oscillation defined as?
a simple repeated motion. when a system moves between 2 points through a mean position over the same period of time
What are two common examples of systems which display simple harmonic motion
a pendulum on a string
a mass spring system
How does energy change as a spring moves through a complete oscillation?
At top : Ep In middle : max Ek At bottom: min Ek In middle: max Ek At top: Ep
Which equation can be used to calculate the time period, T of a mass spring system?
T = 2π x square root of m/k
where k is the spring constant
Which equation can be used to calculate the time period, T of a simple pendulum system?
T = 2π x square root of l/g
where l is the length og the pendulum and g is the acceleration due to gravity
What equation gives the displacement of an object at any given time during simple harmonic motion?
x = Acos(ωt)
How do you calculate the equation for velocity from the equation for displacement? (or acceleration from velocity)
integrate the equation (the area under the curve)
(x = Acos(ωt) becomes v = -ωAcos(ωt))
where A is amplitude
When a free vibration is allowed to oscillate it does so with what?
Natural frequency, f zero
everything has an f0
What is resonance?
When the driving force oscillates at the same frequency as the object, they interfere and the amplitude becomes very large.
How does damping impact the amplitude of an object in resonance?
Large damping = lower amplitude
Light damping = medium amplitude
No damping = large amplitude
On a graph of amplitude against driving frequency, the amplitude is greatest at which point?
f zero (natural frequency)
Which equation can be used to calculate the velocity of an object at any given moment in simple harmonic motion?
v = +or- ω x square root of A^2 - x^2
