Mechanics

Question 1

What is an non-inertial frame of reference ?

Answer 1

A perspective where the fame of reference is accelerating in some way

Question 2

What type of reference frame follows newtons laws of motion ?

Answer 2

An inertial frame of reference

Question 3

What is the derivation from F=dP/dt to F=ma?

Answer 3

F=dP/dt
P=mv
F=d/dt(mv)
F=v(dm/dt)+m(dv/dt)
constant mass and dv/dt=a
F=ma

Question 4

True or False:

Newton 3 Pairs only act between the same body under motion

Answer 4

False

Newton 3 pairs only act between two different bodies of motion

Question 5

Describe a central force

Answer 5

• 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

Question 6

What is the position vector given by in polar coordinates ?

Answer 6

r=r.rhat

Question 7

What are rhat and thetahat given by?

Answer 7

rhat= cos(theta)i+sin(theta)j
thetahat= -sin(theta)i+cos(theta)j

Question 8

What is the equation for velocity in terms of polar coordinates?

Answer 8

V=rdot . rhat+ r . thetadot . thetahat

Question 9

What does the equation for velocity become for constant circular motion?

Answer 9

V= r . thetadot . thetahat 
V= rw . thetahat

Question 10

What happens to the force on an object in the theta direction if acted under by a central force?

Answer 10

F(theta)=0

=> a(theta)=0

Question 11

What happens when a(r)=0?

Answer 11

The object will experience a non uniform circular motion

The object follows a spiral trajectory

Question 12

What are the three key ideas when considering a central force ?

Answer 12

• Motion stays within the plane
• Angular momentum is conserved
• Position vector sweeps out equal areas in equal times

Question 13

What are the equations for work done?

Answer 13

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)

Question 14

True or False:

The work done in dependant upon the path taken for conservative forces

Answer 14

False
The work done in independent for conservative forces
W=integral(F.dr)=0

Question 15

What are some examples of a conservative force?

Answer 15

• Gravity

- Central Force

Question 16

What are the equations for Torque and Angular momentum?

Answer 16

• 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

Question 17

What is the equation for the centre of mass?

Answer 17

R = 1/m(sum(m(i)r(i)))

Question 18

what effect does the internal force between particles in a system have on the net force in the system?

Answer 18

The internal force between particles in the system = 0

So it has no effect on the net force

Question 19

What is the net kinetic energy due to rotation alone ?

Answer 19

Ek(net)= (M r^2 w^2)/4 = 1/2 I w^2

Question 20

What is special about a rigid body?

Answer 20

It does not deform

Question 21

What is the product of inertia about the principle axis ?

Answer 21

0

Question 22

What type of objects will have a principle axis?

Answer 22

Any shape with symmetry will have a principle axis

Question 23

Define the steps for deriving the moment of inertia of a shape

Answer 23

• 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

Question 24

What is the moment of inertia for a rod, thin disc and a sphere?

Answer 24

• I = 1/12 m R^2
• I = 1/2 m R^2
• I = 2/5 m R^2

Question 25

What is the expression for the moment of inertia for a shape about a parallel axis ?

Answer 25

I=I(com)+md^2

Question 26

For an object rolling without slipping, will the acceleration about the centre of mass be greater than , less than or equal to F/m?

Answer 26

a(com) will be greater than F/m