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Jan 7-11: Mon: Rotational Kinematics (Ch. 8.1 - 8.3) Tue: Wed: Torque (Ch. 9.1) Center of Gravity (Ch. 9.3) Thurs: Hookes Law (springs) (Ch. 10.1) Elastic Potential Energy (Ch. 10.3)
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Mon: Rotational Kinematics (Ch. 8.1 - 8.3)
Wed: Torque (Ch. 9.1)
Center of Gravity (Ch. 9.3)
Thurs: Hookes Law (springs) (Ch. 10.1)
Elastic Potential Energy (Ch. 10.3)
Fri: Pendulums (Ch. 10.6)
Jan 21: MLK Day (no school)
Jan 22-25: Finals
Bulls-Eye Lab Practicum
Last three weeks of the Semester…
The angle through which the
object rotates is called the
Θ in rad
ω in rad/s
α in rad/s2
* ω and α might be in rev/s but use dimensional analysis to make sure the equations are “dimensionally balanced”!
Counter-clockwise is usually taken to be positive.
x = x0 + v0 t + ½at2
v = v0 + at
x = ½(v0 + v)t
v2 = v02 + 2ax
v = ½ (v0 + v)
θ = θ0+ ω 0t + ½αt2
ω = ω0 + αt
θ = ½ (ω0 + ω)t
ω2 = ω02 + 2α θ
ω = ½ (ω 0 + ω)
For CONSTANT linear acceleration
For CONSTANT rotational acceleration
The blades of an electric blender are whirling with an angular velocity of 375 rad/s while the “puree” button is pushed in. When the “blend” button is pressed instead, the blades accelerate and reach a greater angular velocity after the blades have rotated an angular displacement of 44.0 rad. The angular acceleration is constant at 1740 rad/s2. Find the final angular velocity of the blades. (‘Blades’ refers to the TIP of the blade at all times.)
Using ω2 = ω02 + 2α θ
v = 541.98 = 542 rad/s
whenθ is in radians
Convert 2 degrees into radians.
Then s = 1.48 x 106 meters
In many of these problems, use proportionalities.
And use dimensional analysis to set up your problems!
And finally, think about them! You often ‘know’ how to solve these.
For instance, a circle has a radius of 4 meters. An object travels on this circular path, and travels a distance of 11 meters. How many radians did it travel?
The distance around the circle one time is 2π4 = 8π= 25.13 m
Proportion: 11/25.13 meters = θ/2 π = 2.75 radians
The diameter of the sun is about 400 times greater than that of the moon. By coincidence, the sun is also about 400 times farther from the earth than is the moon.
For an observer on the earth, compare the angle subtended by the moon to the angle subtended by the sun and explain why this result leads to a total solar eclipse.
Using s = rθ, we can see that the angle is the same in both cases, so the moon is able to completely block the sun!
A gymnast on a high bar swings through
two revolutions in a time of 1.90 s.
Find the average angular velocity
of the gymnast.
Changing angular velocity means that an angular
acceleration is occurring.
Example A Jet Revving Its Engines
As seen from the front of the engine, the fan blades are
rotating with an angular speed of -110 rad/s. As the
plane takes off, the angular velocity of the blades reaches
-330 rad/s in a time of 14 s.
Find the angular acceleration, assuming it to be constant.