Section 1
Preview this deck
Rotation Fact
Front
| 5 | 0 | ||
| 4 | 0 | ||
| 3 | 0 | ||
| 2 | 0 | ||
| 1 | 0 |
Active users
0
All-time users
0
Favorites
0
Last updated
6 years ago
Date created
Mar 1, 2020
Cards (58)
Section 1
(50 cards)
Rotation Fact
Every point on a rotating, rigid surface has the same angular velocity.
Where is the greatest angular Kinetic Energy for a spinning object with changing radius?
Position where angular speed is highest (smallest radius)
What is the slope of a graph of angular position vs time?
angular velocity
Work energy theorem for rotational motion only
Translational Motion
Type of motion where an object starts at one point and moves to another.
**Rotational Kinetic Energy: Work and Energy Revisited
I (Rotating rod at end)
I = 1/3 ML^2
Angular Acceleration
The rate of change of angular velocity in radians/second squared.
Tangential acceleration is directly related to?
Tangential acceleration alpha t is directly related to the angular acceleration alpha and is linked to an increase or decrease in the velocity, but not its direction.
I (solid sphere)
I = 2/5 MR^2
Angular Momentum
The rotational equivalent of linear momentum. A product of moment of inertia and angular velocity, L
Where is the greatest Moment of Inertia for a spinning object with changing radius?
Position where radius is the greatest
What is angular acceleration?
Uniform circular motion: motion in a circular path at constant speed
What is the equation for torque, moment of intertia, and angular acceleration?
The units of moment of intertia are kgm^2 (If you want to give something angular acceleration - you need torque).
Rotational Inertia
(b) At what speed is fishing line leaving the reel after 2.00 s elapses?
Example: A father pushing a playground merry-go-round. He exerts a force of 250 𝑁 at the edge of the 50.0 𝑘𝑔 merry-go-round, which has a 1.50 𝑚 radius. Calculate the angular acceleration produced when no one is on the merry-go-round. Consider the merry-go-round itself to be a uniform disk.
I (hollow sphere or ring)
I = 2/3 MR^2
Example: A powerful motorcycle can accelerate from 0 to 30.0 m/s in 4.20 s. What is the angular acceleration of its 0.320 m radius wheels?
What occurs with angular acceleration when change occurs?
There is an angular acceleration, in which 𝜔 changes. The faster the change occurs, the greater the angular acceleration. -where delta omega is the change in angular velocity and delta t is the change in time. The units of angular acceleration are rad/s2.
What is the equation that shows this relationship?
This equation is the rotational analog of Newton's second law (F=ma ) Torque is analogous to force Angular acceleration is analogous to translational acceleration mr^2 is analogous to mass (or inertia)
**Moment of Inertia and Torque
I (cylinder or disk)
I = 1/2 MR^2
If radius of a rotating object decreases, what happens?
Angular speed increases
Rotational and Translational Quantities
Kinematics of Rotational Motion
What is the relationship between tangential acceleration a(t) and angular accretion (alpha)?
(c) How many revolutions does the reel make?
2 pi
The value you must multiply by to change revolutions to radians.
How do we define angular velocity (omega)?
We defined angular velocity 𝜔 as the time rate of change of an angle theta.
Frequency
The number of rpm, revolutions per minute. Can also be rotations or turns per minute or second.
Law of Conservation of Angular Momentum
Angular Momentum is always conserved.
Example: Suppose a teenager puts her bicycle on its back and starts the rear wheel spinning from rest to a final angular velocity of 250 rpm in 5.00 s. (a) Calculate the angular acceleration in rad/s2. (b) If she now slams on the brakes, causing an angular acceleration of -87.3rad/s2 , how long does it take the wheel to stop?
Angular Velocity
A speed of rotation measured in radians/second.
Main idea of rotational inertia
What is linear or tangential acceleration?
Linear or tangential acceleration, 𝑎𝑡 refers to changes in the magnitude of velocity but not its direction. In circular motion centripetal acceleration, 𝑎𝑐 , refers to changes in the direction of the velocity but not its magnitude.
Angular Displacement
A measure of the amount of radians that an object rotates through.
What happens if omega increases or decreases? What is the angular acceleration (alpha)?
**Dynamics of Rotational Motion: Rotational Inertia
What is the relationship between force, mass, radius and angular acceleration?
To develop the precise relationship among force, mass, radius, and angular acceleration, consider what happens if we exert a force F on a point mass m that is at a distance r from a pivot point
I (Rotating rod at center)
I = 1/12 ML^2
net work (W) = net Fd cos(theta)
What is kinematics? What is kinematics of rotational motion?
Kinematics is the description of motion. The kinematics of rotational motion describes the relationships among rotation angle, angular velocity, angular acceleration, and time.
**Kinematics of Rotational Motion
Rotational Motion
Type of motion where an object "spins in place".
How do you calculate total kinetic energy for an object that is rotating about its axis and moving linearly?
Sum of : Translational KE (1/2 mv^2 ) + Rotational KE (1/2 Iw^2)
**Tangential acceleration and centripetal acceleration
Moment of Inertia
The rotational equivalent of mass, I
What is the slope of a graph of angular velocity vs time?
angular acceleration
Example: A deep-sea fisherman hooks a big fish that pulls line from his fishing reel, which is initially at rest. The reel is given an angular acceleration of 110 𝑟𝑎𝑑/𝑠2 for 2.00 𝑠 and line unwinds from the reel at a radius of 4.50 cm from its axis of rotation. (a) What is the final angular velocity of the reel?
Section 2
(8 cards)