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AP Physics: Rotational Kinematics

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What is the rotational analog for the following translated kinematic equation: (d) x = 1/2(Vi + Vf)t

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Mar 1, 2020

Cards (23)

Section 1

(23 cards)

What is the rotational analog for the following translated kinematic equation: (d) x = 1/2(Vi + Vf)t

Front

θ = 1/2(Wi +Wf)t

Back

Rotation

Front

centrifuges and space stations exhibit a different sort of motion: rotation "spin it in place" *circle with line in the middle -> the center of the object doesn't move, but the outer parts circle around it. radians will be used in this unit on rotation (rotation = arc length / radius)

Back

Newton's 2nd Law for rotation

Front

α = Tnet / I α = angular acceleration (rad/s^2) Tnet = net torque (N-m) I = Moment of Inertia (kg.m^2) *Moment of Inertia is the Rotational Equivalent of Mass

Back

what is d in T=Fd?

Front

d = perpendicular distance from the axis of rotation to the line along which the force acts

Back

a = rα

Front

where... a = acceleration (m/s^2) r = radius (m) α = angular acceleration (radians/s^2) every point on a rotating rigid body has the same angular velocity, W

Back

For a rigid body, each particle has the same angular acceleration, α

Front

look at diagram in notes T1 = m1r1^2α T2 = m2r2^2α T3 = m3R3^2α Tnet = (m1r1^2 + m2r2^2) +m3r3^2)α or SIGMA miri^2

Back

formula for torque, force, and distance

Front

T = Fd T - torque (N-m) F - Newtons d = perpendicular distance (m)

Back

How to convert revolutions to radians vs how to convert radians to revolutions?

Front

multiply by 2PI vs divide by 2PI

Back

What is the rotational analog for the following translated kinematic equation: vf^2 = Vi^2 + 2αx(d)

Front

Wf^2 = Wi^2 +2αθ

Back

Conditions for Equilibrium

Front

1st condition: SFx=0 and SFy=0 2nd condition: ST=0 (rotational equilibrium) *S stands for sigma

Back

v=rW

Front

where... v = linear velocity (m/s) r = radius (m) W = angular velocity (radians/s)

Back

Connection of sign of torque and rotation

Front

We shall use the convention that the sign of the torque resulting from, a force is positive if its turning tendency is counterclockwise negative if its turning tendency is clockwise

Back

What is the rotational analog for the following translated kinematic equation: (d) x = Vit + 1/2at^2

Front

θ = Wit +1/2αt^2

Back

How far? (rotational quantities)

Front

look at diagram in notes x (d)= displacement (meters) θ= angular displacement (radians)

Back

How does velocity change?

Front

a = acceleration (m/s^2) fish looking thing = angular acceleration (radians/ sec^2)

Back

How fast? (rotational quantities)

Front

v = velocity (m/s) W = angular velocity (radians/sec)

Back

Torque causes an angular acceleration formula

Front

α = T / mr^2 α = rad/s^2 T = torque, N-m m = kg r = m

Back

Rotation vs. translation

Front

rotation - centrifuges and space stations exhibit a different sort of motion translation - most situations we have considered so far involve this type of motion

Back

Picking the axis of rotation?

Front

It doesn't matter where you pick the axis of rotation for calculating the new torque if the object is in equilibrium since the object is not rotating, the location of axis is completely aribitrary

Back

Translation

Front

most situations we have considered so far involve the type of motion called translation: "pick it up and put it down somewhere else" *picture of car moving from one spot to the next

Back

Torque

Front

the ability of a force to rotate a body about some axis is measured by a quantity called Torque

Back

What is the rotational analog for the following translated kinematic equation: Vf = Vi + at

Front

Wf = Wi + αt

Back

Rotational Quantities

Front

for each translational quantity, there is a corresponding rotational quantity: -how far? -how fast? -how does velocity change?

Back