Rotational Kinetic Energy
The formula for rotational kinetic energy
K = 1/2Iω^2
The formula for rotational work
W = τθ
The formula for angular momentum
L=Iω
The formula for conservation of angular momentum
I1ω1 = I2ω2
A rolling body has which two types of energy
Transnational and rotational
Angular kinetic energy is treated as what
A system (group or rigid body)
To imply the most amount of torque, you have to push either closest, to the middle, or furthest away from the point of rotation.
Furthest away.
The formula for angular impulse.
ΔL= τΔt
If the radius of a rotating object increases, what variable of momentum also increases?
Inertia.
The formula to calculate total kinetic energy of a rolling body
Ktot = 1/2mv^2 + 1/2Iω^2
If the angular velocity of a circular system is increased, the kinetic energy will what
Increase (quadruple because it is squared)
On a torque x angular displacement graph, how do you find work?
Slope
A person moves from the center of mass rotating around an axis to the edge of the mass. He experiences the same momentum, however he is experiencing less what
angular velocity
An ice skater experiences more / less velocity when pulling their arms in. Explain.
More. The radius is decreased which decreases the rotational inertia allowing for angular velocity to increase in order to follow the rules of conservation of momentum.
A circle and a block are both moving with the same transitional energy. Which has more total kinetic energy and why?
The cylinder because the kinetic energy is split between transitional and angular kinetic energy.
If the radius decrease on a circular system, the kinetic energy will what
Decrease
Two objects experience the same amount of work. However, object one rotates over distance 1/2 θ and the object two rotates over distance θ. Which object experienced more torque.
Object 1
Angular impulse can be calculated using what on a torque v time graph?
Area under the curve.
Imagine a child on a rotating surface. He is standing at the edge of the surface and proceeds to walk to the center of mass of the rotating surface. Does the velocity of the rotating mass increase, decrease, or remain constant.
Derive the final transitional velocity of a cylindrical shell (without mass) moving down a ramp.
√((2/3) * g * h)
A windmill blade with a rotational inertia of 6.0kg x m^2 has an initial angular velocity of 8 rad/s. Then, it is given angular acceleration of 4.0 rad/s^2 for 10s. What is the change in kinetic energy over the time interval?
6720J
One end of a string is wrapped around a pulley that is free to rotate about its axis at the center. The other end of the string is attached to a block. The block is released from rest and moves at a constant acceleration downward. Does the work done by the pulley remain constant, decrease, or increase.
Constant
A force of magnitude F is exerted tangentially to the edge of a horizontal disk of radius R. The force is exerted over a time interval t, during which the disk rotates over an angle of n/2 radians. What is the change in angular momentum of the disk over this time interval.
FRΔt
A disk with a rotational inertia of 1.8 is rotating counterclockwise with angular velocity of 6 rad/s. A second disk with rotational inertia of 1.2 is rotating clockwise with angular velocity of 6 rad/s when it drops directly on top of the 1st disk. The two disks rotate together without slipping. What is the new angular speed of the disks.
1.2 rad/s
A cylinder and a block have equal masses and are both released from atop a ramp with equal heights. The cylinder rolls without slipping and the block slides with negligible friction. Which of the following objects will have a greater transitional speed and why?
The block because all of the kinetic energy will go into transitional speed instead of splitting between angular velocity and transitional speed.