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23 Rotational Kinematics

# 23 Rotational Kinematics - Rotational coordinates are s = r...

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OLD EQUATIONS v f = v i + at x f = x i + v i t + 0.5at 2 v f 2 = v i 2 + 2a(x f – x i ) x f = x i + 0.5(v i + v f )t NEW EQUATIONS ϖ f = ϖ i + α t θ f = θ i + ϖ i t + 0.5 α t 2 ϖ f 2 = ϖ i 2 + 2 α ( θ f θ i ) θ f = θ i +0.5( ϖ i + ϖ f )t r s = θ r v t = ϖ r a t = α Rotational coordinates are: Therefore:
A vehicle is traveling counterclockwise in a circle (r=40m) at a constant speed of 10m/ s. At the moment shown below, what is the vehicle’s angular acceleration?

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A vehicle is traveling counterclockwise in a circle (r=40m) at a constant speed of 10m/ s. At the moment shown below, what is the vehicle’s angular velocity?
A vehicle is traveling counterclockwise in a circle (r=40m) at a constant speed of 10m/ s. At the moment shown below, the driver hits the brakes. If the car stops after ¼ revolutions around the track, what angular acceleration did the brakes provide?

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A vehicle is traveling counterclockwise in a circle (r=40m) at a constant speed of 10m/ s. At the moment shown below, the driver hits the brakes. If the car stops after ¼ revolutions around the track, what tangential acceleration did the brakes provide?
A top spins around 10 times every second. There is a red mark on the top 5cm from the center. How fast is the mark moving?

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A top spins around 10 times every second. If the top stops after 1 minute, what is its angular acceleration?
A top spins around 10 times every second. There is a red mark on the top 5cm from the center. If the top stops after 1 minute, what is the tangential acceleration of the red mark?

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You are in the 8m-diameter spinning fair ride below, traveling at 2m/s. The controller
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