Rotational KE
What is the formula for rotational KE?
KE=(1/2)I(omega)^2
What are the equations for work (in rotational form) and torque?
W=torque*delta(theta) OR W=delta(KE)
Torque=rFsin(theta) OR Torque=Ia
Which two variables are needed for there to be angular momentum?
Rotational inertia and angular velocity
A block and a ball of identical masses are both placed on the same ramp. They are released at the same time, the block slides down the ramp and the ball rolls (without slipping) down the ramp. In terms of energy, why does the block reach the bottom first?
The block only has translational KE, whereas the ball has both translational and rotational KE
A satellite is in a perfectly circular orbit around the earth. What is the work done by the gravitational force on the satellite in the satellite system?
There is none because the velocity and the force of gravity make a 90 degree angle, therefore making cos=0 and W=0.
True or False: an object can have both translational and rotational KE.
True
On a torque vs. angle graph, how do you find the work done?
Find the area under the curve
What is angular impulse, and what causes it?
A change in the angular momentum, and a net external torque acting on an object
In a system that has greater rotational inertia, what will happen to its translational and rotational KE if it rolls without slipping?
The translational KE will decrease, and the rotational KE will increase.
If a satellite is experiencing an elliptical orbit, what is the satellite's torque and change in angular momentum?
Both 0 because the force of gravity and radius vectors are parallel, allowing there to be no net torque. If the net torque is zero, the change in angular momentum must also be zero.
A disk has a mass of 0.65-kg and a radius of 0.4 meters spinning in place with an angular velocity of 5 rad/s. What is the disk's rotational KE?
0.65 J
A wheel with radius 0.54 m and rotational inertia 4.0 kg*m^2 spins on an axle with an initial angular speed of 6.0 rad/s. Friction in the axle exerts a torque on the wheel, causing the wheel to stop after 3.0 s. What is the magnitude of the average torque exerted on the wheel (round to the nearest hundredth)?
8.0 N*m
The wheel on a vehicle has a rotational inertia of 5.0 kg*m^2. At the instant the wheel has a counterclockwise angular velocity of a 6.0 rad/s, an average counterclockwise torque of 7.0 N*m is applied, and continues for 3.0 s. What is the change in angular momentum of the wheel?
21 kg*m^2/s
Derive an expression for the final linear velocity of a solid cylinder with rotational inertia of (1/2)mr^2. Begin with the conservation of energy, and assume the sphere is rolling without slipping.
v=sqrt((4/3)gh)
A satellite moves from point A to point B throughout its elliptical orbit. Point B is closer to the earth than point A. At which point is the linear velocity greater?
Point B
Which has more rotational KE: a hoop or a disk and why?
A hoop, because it's mass is distributed further from the axis of rotation, so it has more rotational inertia, therefore increasing the rotational KE.
In what three scenarios does an object have a net torque of 0?
1. There is no external force
2. The force is acting directly on or parallel to the pivot point
3. The torque forces cancel out (same magnitude, different directions)
How can you change the angular speed of an object without changing the angular momentum of that object?
You change the shape so that its mass is closer to the axis of rotation
When an object rolls with slipping, what happens to the total energy in the system and why?
Some of the mechanical energy dissipates due to the friction of the surface, leaving the system with less energy than it began with
A rocket is attempting to leave the earth. To do so it must reach what is called an "escape velocity". What must happen to the KE and PE of the system as the rocket leaves in order to reach escape velocity?
The KE and PE must cancel each other out so the rocket doesn't have any energy when it reaches where it needs to go.
Which of the following pairs will result in the greatest rotational KE? (The w's represent the omega symbol).
- (I) (w) A
- (I) (4w) B
- (2I) (2w) C
- (6I) (w) D
B - (I) (4w)
A uniform rod of mass M and length L is free to rotate about a pivot at its left end and is released from rest when the rod is 43 degrees below the horizontal. With respect to the pivot, the rod has rotational inertia I=(1/3)ML^2. Find the expression that correctly represents the magnitude of the net torque exerted on the rod about the pivot at the moment the rod is released.
MgL/2sin(47)
If you get into a car wreck, the front of the car is designed to do what to protect you and why?
Crumple, because it lengthens your impulse time, therefore decreasing the force that you get hit with
A sphere of mass 2m and radius 6r rolls without slipping down a ramp that makes an angle theta with the horizontal. The magnitude of the acceleration of the center of mass of the sphere is a while the sphere rolls down the ramp. Find the expression that gives the magnitude of the angular acceleration of the sphere.
a=a/6r
When the object is defined to be an infinite distance from the central object in space, what is the gravitational potential energy of the system?
Zero