PHYSICS Ch. 6 Rotational Motion

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Last updated 10:50 PM on 5/14/26
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18 Terms

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angle of rotation

Δθ = Δs / r

Δθ = angle of rotation

Δs = arc length

r = radius

<p>Δθ = Δs / r</p><p></p><p>Δθ = angle of rotation</p><p>Δs = arc length</p><p>r = radius</p>
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Centripetal acceleration

⃗ac = ⃗v2 / r

⃗a = centripetal acceleration (m/s2)

⃗v = velocity (m/s)

r = radius (m)

<p>⃗a<sub>c</sub> = ⃗v<sup>2</sup> / r</p><p></p><p>⃗a = centripetal acceleration (m/s2)</p><p>⃗v = velocity (m/s)</p><p>r = radius (m)</p>
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net force of an object moving in a circular motion

mv2/r

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uniform circular motion

  • net force, velocity, and acceleration are all constantly changing because the object is changing directions

  • kinetic energy is constant in a uniform circular motion because the object’s speed is constant and does not change based on its position on the circular path

<ul><li><p>net force, velocity, and acceleration are all constantly changing because the object is changing directions</p></li><li><p>kinetic energy is constant in a uniform circular motion because the object’s speed is constant and does not change based on its position on the circular path</p></li></ul><p></p>
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Centrifugal force

an apparent force, directed outwards, experienced by an object travelling in a circular path

<p>an apparent force, directed outwards, experienced by an object travelling in a circular path</p>
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centripetal force

a force that keeps an object moving in a circular motion. It is a real force and directed towards the center of the circular path

<p><span>a force that keeps an object moving in a circular motion. It is a real force and directed towards the center of the circular path</span></p>
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When a car is travelling around a circular path, _________ will be the centripetal force that acts to prevent the car from sliding off the road.

friction

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the direction of linear velocity and centripetal acceleration are ______ to each other

perpendicular

If the centripetal force is removed, the object will travel in a linear path perpendicular to the circular path it was originally on

<p>perpendicular</p><p>If the centripetal force is removed, the object will travel in a linear path perpendicular to the circular path it was originally on</p>
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Torque

τ = rFsinθ

τ = torque (kg m2⋅s-2)

r = radius (m)

F = force (N)

θ = angle between force and lever arm

<p>τ = rFsinθ</p><p></p><p>τ = torque (kg m<sup>2</sup>⋅s<sup>-2</sup>)</p><p>r = radius (m)</p><p>F = force (N)</p><p>θ = angle between force and lever arm</p>
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Rotational kinematics

ωf = ω0 + αt

θ = ω0t + 1/2αt2

ω2 = ω02 + 2αθ

θ = angle of rotation

ω0 = initial angular velocity (rad/s)

ωf = final angular velocity (rad/s)

t = time (s)

α = angular acceleration (rad/s2)

<p>ω<sub>f</sub> = ω<sub>0</sub> + αt</p><p>θ = ω<sub>0</sub>t + 1/2αt<sup>2</sup></p><p>ω<sup>2</sup> = ω<sub>0</sub><sup>2</sup> + 2αθ</p><p></p><p>θ = angle of rotation</p><p>ω<sub>0</sub> = initial angular velocity (rad/s)</p><p>ω<sub>f </sub>= final angular velocity (rad/s)</p><p>t = time (s)</p><p>α = angular acceleration (rad/s<sup>2</sup>)</p>
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Period

T = 2π/ω

T = period

ω = angular velocity (rad/s)

f = frequency (s-1)

<p>T = 2π/ω </p><p></p><p>T = period</p><p>ω = angular velocity (rad/s)</p><p>f = frequency (s<sup>-1</sup>)</p>
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angular velocity

ω = Δθ / Δt

angular displacement (Δθ rad) per unit of time (Δt s)

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Moment of inertia

I = mr2 for hoop about cylinder axis

I = mr2 / 2 for solid cylinder (or disk) about cylinder axis

I = 2mr2 / 5 for solid sphere about any diameter

I = moment of inertia (kg⋅m2)

m = mass of rotating bodies (kg)

r = distance of object from centre of axis of rotation (m)

<p>I = mr<sup>2</sup> for hoop about cylinder axis</p><p>I = mr<sup>2 </sup>/ 2 for solid cylinder (or disk) about cylinder axis</p><p>I = 2mr<sup>2 </sup>/ 5 for solid sphere about any diameter</p><p></p><p>I = moment of inertia (kg⋅m<sup>2</sup>)</p><p>m = mass of rotating bodies (kg)</p><p>r = distance of object from centre of axis of rotation (m)</p>
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Newtons law of universal gravitation force

Fg = GMm / r2

Fg = gravitational force (N)

G = universal gravitational constant (6.67x10-11 Nm2/kg2)

M = mass of object 1 (kg)

m = mass of object 2 (kg)

r = distance of body from the center of the earth (m)

<p>F<sub>g</sub> = GMm / r<sup>2</sup></p><p></p><p>F<sub>g</sub> = gravitational force (N)</p><p>G = universal gravitational constant (6.67x10<sup>-11</sup> Nm<sup>2</sup>/kg<sup>2</sup>)</p><p>M = mass of object 1 (kg)</p><p>m = mass of object 2 (kg)</p><p>r = distance of body from the center of the earth (m)</p>
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Newtons law of universal gravitation force

a = τnet / I

α = angular acceleration (rad/s2)

τ = torque (N⋅m)

I = moment of inertia (kg⋅m2)

<p>a = τ<sub>net</sub> / I</p><p></p><p>α = angular acceleration (rad/s<sup>2</sup>)</p><p>τ = torque (N⋅m)</p><p>I = moment of inertia (kg⋅m<sup>2</sup>)</p>
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angular momentum

L = Iω

L = angular momentum (kg * m2 / s)

I = inertia (kg * m2)

ω = angular velocity (rad/s)

drop the “rad” for radians when expressing the units for angular momentum because a radian is the ratio of arc length to radius; it is an expression of proportionality, not a physical unit in itself.

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escape velocity

ve = sqrt( 2Gmp / rp )

escape velocity is dependent on the gravitational constant, G, the mass of the planet, mp, and the radius of the planet rp

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conservation of momentum

Li = Lf