Circular motion and angular momentum

Question 1

What relates the linear velocity to the angular velocity?

Answer 1

v=ωr

Question 2

What relates the linear velocity vector to the angular velocity vector?

Answer 2

v=ωxr
Where x means the cross product and r is the position vector from an origin that lines on the axis of rotation

Question 3

What is the centripetal acceleration?

Answer 3

a=ωv=ω^2r=v^2/r

Question 4

What is the torque?

Answer 4

τ=rxF
Where x means cross product

Question 5

How do you balance moments?

Answer 5

F1r1=F2r2

Question 6

What is angular momentum?

Answer 6

L=rxp
Where x means cross product and p is the momentum

Question 7

What relates torque and angular momentum?

Answer 7

τ=dL/dt=Idω/dt=Id^2θ/dt^2
Torque equals the rate of change of angular momentum

Question 8

What is the moment of inertia?

Answer 8

I=mr^2

Question 9

How do angular momentum and the moment of inertia relate?

Answer 9

L=Iω=mrv=mr^2ω

Question 10

What is the rotational kinetic energy?

Answer 10

T=1/2Iω^2

Question 11

What torque does a force acting towards the centre of rotation generate?

Answer 11

None

Question 12

What is the velocity for an circular orbit?

Answer 12

V^2=GM/R

Question 13

How is the moment of inertia calculated?

Answer 13

I=∫r^2 dm=I=∫r^2pdV
Where p is the desnity

Question 14

what are some example moments of inertia?

Answer 14

For a hollow sphere about an axis through its centre I=2/3 MR^2
For a solid sphere about an axis through its centre I=2/5 MR^2
Thin rod, length L about a perpendicular axis through its centre I=1/12 ML^2
Thin rod, length L about a perpendicular axis through one end I=1/3 ML^2

Question 15

What is the parallel axis theorem?

Answer 15

Moment of inertia for an object mass M around an axis that lies a distance d from a parallel axis that pass through the centre of mass, is the moment of inertia about that axis plus Md^2
I(any axis)=I_cm(||)+Md^2