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AP Physics 1: Rotational Motion and Torque
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Gravity
Terms in this set (32)
circumference of a circle
angular displacement
angle the object rotates through during some time interval (θ- theta)
equation for angular displacement (θ)
s=arc length
r= radius
units: radians
to convert degrees to radians and vice versa
multiply by π/180 or 180/π
angular speed
ratio of angular displacement to time interval (ω- omega)
equation for angular speed (ω)
units: rad/s
instantaneous angular speed
the limit of the average speed as the time interval approaches zero
avg. angular acceleration
the ratio of the change in the angular speed to the time it takes for the object to undergo the change (α- alpha)
equation for angular acceleration (α)
units: rad/s²
rotational motion kinematics equations
ω=ωi + αt
∆θ=ωit + 1/2αt²
ω²=ωi² + 2α∆θ
period
time it takes for object in circular motion to make 1 complete revolution, or cycle
-measured in seconds
frequency
number of cycles in 1 second
-measured in 1/sec or sec⁻¹, aka Hz (Hertz)
f=1/T
equation #1 for centripetal acceleration
equation #2 for centripetal acceleration
a= rω²
forces that cause centripetal acceleration
-level curves
-banked curves
-horizontal curves
-vertical curves
level curves vs. banked curves
-level: friction is force that produces centripetal acceleration
-banked: component of normal force adds to frictional force to allow higher speeds
center of gravity
geometric center of object
-must lie on the axis of symmetry
how to find center of gravity
sum of each mass times its distance then divide by sum of masses
torque
tendency of a force to rotate an object about some axis
-factors: magnitude of force, position of application of force, angle at which force is applied
equation for torque
T= r⊥F
f- force perpendicular to lever
r- length of lever arm
Units: Nm
torque direction
counterclockwise=positive
clockwise=negative
net torque
subtract clockwise (negative) torque from counterclockwise (negative) torque
axis of rotation
if object is in equilibrium, it doesn't matter where you put axis of rotation for calculating net torque
solving equilibrium problems
1. Draw a picture showing forces acting.
2. Choose a convenient axis of rotation.
-Since there is no net rotation, this axis can be anywhere
3. Show distances to the axis of rotation to each force acting.
4. Apply the First Condition of Equilibrium
-This will give you 2 equations (Horizontal and vertical)
-All of the forces acting should add up to zero
5. Apply the Second Condition of Equilibrium
-All of the torques should add to zero
6. Solve the resulting simultaneous equations for all of the unknowns
-Solving by substitution is generally easiest
I = "moment of inertia"
-consider mass, shape, and axis of rotation
equations for I
varies w/shape
-for particle: I= mr^2
equation for torque using I
T=Iα
rotational kinetic energy
conservation of rotational kinetic energy
TMEi=TMEf
(KEr+KEt+PEg+PEs)i = (KEr+KEt+PEg+PEs)f
rotational momentum
L=Iω
units: kgm²/s
torque in terms of momentum
∆L/∆t
conservation of angular momentum
initial angular momentum equals final angular momentum when net torque on system is zero
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