Further Mechanics Flashcards
Circular Motion , Simple Harmonic Motion , Free and Forced Vibrations and Damping
Define angular speed (ω) in words
The angle an object rotates through per second
Give the equation for angular speed
ω = Θ / t
What are the units for angular speed?
rad s^-1
What is the equation that links angular speed and linear speed?
ω = v / r
ω = angular speed
v = linear speed
r = radius
For an object in circular motion do all points have the same angular speed?
Yes, because all points turn throught the same angle each second
For an object in circular motion do all points have the same linear speed?
No , because as v = ωr increases, the ω stays constant as v increases with r
Give the equation that links angular speed (ω) to frequency (f)
ω = 2πf
Give the equations that links angular speed (ω) to time periord (T)
ω = 2π / T
State the direction of the velocity for an object in circular motion
At a tangent to the circle
Explain why an object in unifrom circular motion is accelerating
Velocity is a vector quantity so it has magnitude and direction. The velocity is constantly changing as the direction is changing. The object is therefore accelerating as a = Δv / Δt
In which direction does centripetal force acceleration act in ?
Towards the center of the circle
What are the two equations for centripetal acceleration?
a = v ^2/ r = ω^2r
Explain why a resultant force must be acting on an object in circular motion (Refering to Newton’s laws)
Newton’s 2nd law states that the resultant force on an object is directly proportional to acceleration (F=ma) and direction. As the object is accelerating , a resultant foece called the centriperal force must be acting upon the object.
Which direction does centripetal force act in?
Towards the center of the circle
Give two equations for centripetal force
F = mv^2/r = mω^2r
How do you work out the centripetal force on an object?
Draw the forces acting on the object (eg. tension and weight), determine the resultant force towards the center of the circle (e.g T-W or T+W)
For a particle moving in a circle with uniform speed , is its kinetic energy constant?
Yes, because K.E is a scalar quantity
For a particle moving in a circle with uniform speed , is its momentum constant?
Constantly changing as momentum is a vector quantity and direction of velocity is constantly changing
If the centripetal force is suddenly removed, what will happen to the motion of the object?
Object will move off at tangent to the circle.
For an object in uniform circular motion, is work done by the centripetal force on the object? Explain why or why not?
No work done by the centripetal force as the foce is perpendicular to the displacement and W = FsCosΘ , so if Θ = 90 , cos Θ = 0 and W = 0J
