Reading...
Play button
Play button
Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
34 Cards in this Set
- Front
- Back
|
Torque Concept
|
Rotational Force, description of linear force around a radius (r)
|
|
|
Torque Equation
|
t = τ = r F sinθ
∑τ = Iα Torque is also the derivative of angular momentum: ∆τ = ∆L/∆t |
|
|
What two kinds of Linear acceleration exist?
|
There is tangential and centripetal acceleration!
If both exist, then do vector addition of the accelerations! |
|
|
How do you compute tangential acceleration?
|
At = rα
|
|
|
How do you compute centripetal acceleration?
|
Acp = rω²
|
|
|
What is the concept of Center of Mass (CM)? and why is it special?
|
The CM is the weighted average of an object and it follows rules of a point particle
|
|
|
How do you compute Center of Mass?
|
Xcm = ∑mr / M
|
|
|
What is rigid body rotation? Describe the motion
|
Each point in an object goes in a circle
ω and α are common to each point on an object |
|
|
What is the concept of Angular Velocity?
|
Change in angular position over time
|
|
|
How do you determine the direction of motion for Angular Velocity?
|
Right Hand Rule: curl fingers in direction of motion and thumb points in direction of ω
|
|
|
How does Angular Velocity relate to Centripetal Acceleration?
|
Acp = rω²
|
|
|
How does Angular Velocity relate to Linear velocity?
|
Vt = rω
|
|
|
What are the basic equations to find Angular velocity?
(Analog of linear velocity) |
ω = ∆θ/ ∆t
ω = ω۪ + αt θ = θ + ω۪ t + αt²/2 ω² = ω۪ ² + α(∆θ) |
|
|
What is Angular Acceleration?
|
Change in angular velocity over time
The analog of linear acceleration |
|
|
How do you compute angular acceleration from tangential acceleration?
|
At = rα
|
|
|
What is Inertia?
|
Describes amount of resistance to changes in its rotational Motion.
The analog of linear mass |
|
|
What will affect Inertia to be bigger or smaller?
|
Depends on object and its axis of rotation!
Depends on how mass is distributed, if mass is concentrated at end, the inertia will be larger than if it was evenly distributed! Inertia different, if the axis is on the CM. Have to use constant for each type of shape!!! |
|
|
What happens if an object has a smaller inertia?
|
The object is easier to rotate!
|
|
|
What is the equation for Inertia?
|
I = ∑mR²
|
|
|
What two types of movement are involved in rotating objects?
|
Rotational and translational motion
|
|
|
Why is friction important for rotational motion?
|
The effect of friction makes the object spin instead of slide. This allows the rotational motion
|
|
|
What equation describes rotational motion?
|
K = 1/2 mv² + 1/2 Iω²
K = 1/2 mv²( 1 + 1/(mr²)) |
|
|
In a race of Ball, Hoop and Cylinder: which wins the race down a ramp?
Why? |
The object with the smallest moment of inertia wins, takes less energy to rotate
This is the object with the smallest radius →want velocity to be big and radius to be small! → The Ball wins the race! |
|
|
How is velocity described in Rotational and translational movement?
|
For rotation: each velocity is tangent to circle
For translation: every particle is moving in same velocity direction Combined motion: 1. Zero velocity at bottom bc they cancel out 2. CM only describes translational motion, bc its like a point particle!' 3. everything else is a combination of velocity vectors! |
|
|
How do you determine the direction of Torque?
|
Right hand Rule: curl fingers in direction of force on object and thumb points in direction of torque
|
|
|
Example: How would you find the tension in a Hanging weight supported by rod and string?
(Torque is involved!) |
The pin on the wall and bar is a good reference point
There are torques in the y direction coming from the weights (Bar and mass) and tension from string The sign is not rotating so the net torque is zero! Add all torques together, using r relative to pin reference point = zero Solve for unknown T tension |
|
|
Explain the Bicycle Wheel that spins around axle but does NOT fall vertically from String!
|
The wheels spins while entire system stays horizontal
Angular momentum keeps changing bc direction keeps changing! The torque is not zero! The torque changes with L and t! Fgrav = F tens, so vertical forces cancel out! T The net angular momentum vector moves upward and keeps the wheel horizontal |
|
|
Describe the acceleration of this system: A weight hanging from a pulley
|
The Total Force equals the Tension of the string minus the wieght ∑F = T -mg= ma
The Torque of the tension can be calculated as: τ = Iα, (and τ=rF) so -TR=Iα Plug in a/r for α, so -TR = Ia/R Finally, a= -g/(1 + 1/(mr²)) |
|
|
What is Angular Momentum? How is it conserved?
|
Angular momentum is the extent to which the object will continue to rotate about that point unless acted upon by an external torque.
If net torque is zero, Angular momentum is conserved! |
|
|
How do you determine the direction of angular momentum?
|
Right Hand Rule: curl fingers in direction of motion and thumb points in direction of L
|
|
|
How do you compute angular momentum?
|
L = I ω
L = rmvsinθ |
|
|
What is the conservation of angular momentum equation?
|
Li = Lf (if net torque = 0)
|
|
|
What is the angular momentum impulse theorem?
|
Iωi +∑τ∆t = Iωf
|
|
|
How do you compute Angular collisions?
|
Use conservation of angular momentum! Break down L to L = I ω
|
