Mechanics Flashcards
What is an non-inertial frame of reference ?
A perspective where the fame of reference is accelerating in some way
What type of reference frame follows newtons laws of motion ?
An inertial frame of reference
What is the derivation from F=dP/dt to F=ma?
F=dP/dt P=mv F=d/dt(mv) F=v(dm/dt)+m(dv/dt) constant mass and dv/dt=a F=ma
True or False:
Newton 3 Pairs only act between the same body under motion
False
Newton 3 pairs only act between two different bodies of motion
Describe a central force
- This is where the velocity and the force of two or more particles form a plane
- Any acceleration under a central force is confined to the plane created by v and F
- And hence the motion of the object is confined to the plane as well
What is the position vector given by in polar coordinates ?
r=r.rhat
What are rhat and thetahat given by?
rhat= cos(theta)i+sin(theta)j thetahat= -sin(theta)i+cos(theta)j
What is the equation for velocity in terms of polar coordinates?
V=rdot . rhat+ r . thetadot . thetahat
What does the equation for velocity become for constant circular motion?
V= r . thetadot . thetahat V= rw . thetahat
What happens to the force on an object in the theta direction if acted under by a central force?
F(theta)=0
=> a(theta)=0
What happens when a(r)=0?
The object will experience a non uniform circular motion
The object follows a spiral trajectory
What are the three key ideas when considering a central force ?
- Motion stays within the plane
- Angular momentum is conserved
- Position vector sweeps out equal areas in equal times
What are the equations for work done?
W=F . S
W=F.S.cos(theta)
W=integral(F.dr)=integral(Fx.dx)+integral(Fy.dy)+integral(Fz.dz)
W=integral(Fr.dr)+integral(Ftheta.r.dtheta)
W=detaEk
W=integral(F.V.dt)
True or False:
The work done in dependant upon the path taken for conservative forces
False
The work done in independent for conservative forces
W=integral(F.dr)=0
What are some examples of a conservative force?
- Gravity
- Central Force
What are the equations for Torque and Angular momentum?
- Torque = r x F = I alpha
- L=r x P = r x mv = mr^2w
Torque and L depend upon the reference frame being used
What is the equation for the centre of mass?
R = 1/m(sum(m(i)r(i)))
what effect does the internal force between particles in a system have on the net force in the system?
The internal force between particles in the system = 0
So it has no effect on the net force
What is the net kinetic energy due to rotation alone ?
Ek(net)= (M r^2 w^2)/4 = 1/2 I w^2
What is special about a rigid body?
It does not deform
What is the product of inertia about the principle axis ?
0
What type of objects will have a principle axis?
Any shape with symmetry will have a principle axis
Define the steps for deriving the moment of inertia of a shape
- Set I = sum( r(i)^2 dm ) where r(i) and dm is from splitting the rod into little mass elements
- Set the linear density of the object (say mass per unit length ) dm = lambda dr
- Substitute this in and now integrate with respect to r
- Solve the integral and now rearrange to sub back in the original mass and length of the object
What is the moment of inertia for a rod, thin disc and a sphere?
- I = 1/12 m R^2
- I = 1/2 m R^2
- I = 2/5 m R^2
What is the expression for the moment of inertia for a shape about a parallel axis ?
I=I(com)+md^2
For an object rolling without slipping, will the acceleration about the centre of mass be greater than , less than or equal to F/m?
a(com) will be greater than F/m
