Equations to Remember
Important Key Points
Miscellaneous
Vocab to Know
100
What expression do we use to relate linear and angular acceleration?
a=ralpha
100
The torque of a force depends on what three things?
1. The magnitude of the force
2. The distance of the force from the pivot
3. The angle between the force and radial direction
100
Gravity will only exert a net torque on an object if what is true?
The object is pivoted somewhere other than its center of mass.
100
What is angular velocity?
The rate of change of angle/angular position (or angular displacement over time)
200
Write the expression we use to set up the integral when calculating the rotational inertia of a solid. (Hint - what do we substitute into the integral?)
lambda=M/L=(dm)/(dr)
200
What must be true for any object in equilibrium?
The net force is zero AND the net torque is zero.
200
What is the equation which connects torque and angular momentum?
DeltaL=tauDeltat
200
What is a point mass and how do we calculate its angular momentum ?
An object with mass but negligible shape or size. (L=rp=rmv)
300
What is the mathematical expression for the parallel axis theorem and when do we use it?
I=I_(cm)+md^2
When we know the rotational inertia about one axis, but want it through another axis
300
A disk has a rotational inertia of:
I_0
If the radius of the disk doubles and the mass of the disk triples, what is the new rotational inertia of the disk?
I=12I_0
300
Draw a force diagram showing all the forces acting on the rod below.
300
A bike operates by connecting the driven pedal to a gear connected to the wheel. What must be true about the motion of the pedal gear and the wheel gear?
The edge of each gear must have the same linear (or tangential) velocity
400
What is the rotational inertia of a cylinder (or disk) or mass M and radius R about its center?
I=1/2MR^2
400
A ball is swinging in a circle at a constant angular velocity. Write an expression relating the tension in the string to the angular velocity.
a_c=v^2/r=omega^2r; T=momega^2r
400
A satellite is spinning in space with an angular momentum
L_0
and a rotational kinetic energy
K_0
If the satellite extends its solar panels such that the rotational inertia of satellite increases by a factor of 4, what is the new angular momentum and rotational kinetic energy of the satellite?
L=L_o, K=1/4K_0
400
A rod of mass M and length L is pivoted to a wall and released from a horizontal position. What is the angular acceleration of the rod?
About the pivot, the rod has a rotational inertia of:
I=1/4ML^2
alpha=(2g)/L