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Unformatted text preview: Physics 6A Rotational Motion Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB First some quick geometry review: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB θ r x = rθ We need this formula for arc length to see the connection between rotational motion and linear motion. We will also need to be able to convert from revolutions to radians. There are 2π radians in one complete revolution. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB θ r x = rθ Definitions of angular velocity and angular acceleration are analogous to what we had for linear motion. Angular Velocity = ω = t ∆ θ ∆ Angular Acceleration = α = t ∆ ϖ ∆ This is the Greek letter omega (not w) This is the Greek letter alpha (looks kinda like a fish) Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB θ r x = rθ Definitions of angular velocity and angular acceleration are analogous to what we had for linear motion. Angular Velocity = ω = t ∆ θ ∆ Angular Acceleration = α = t ∆ ϖ ∆ This is the Greek letter omega (not w) Example: A centrifuge starts from rest and spins for 7 seconds until it reaches 1000 rpm. Find the final angular velocity and the angular acceleration (assume constant). This is the Greek letter alpha (looks kinda like a fish) Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB θ r x = rθ Definitions of angular velocity and angular acceleration are analogous to what we had for linear motion. Angular Velocity = ω = t ∆ θ ∆ Angular Acceleration = α = t ∆ ϖ ∆ This is the Greek letter omega (not w) Example: A centrifuge starts from rest and spins for 7 seconds until it reaches 1000 rpm. Find the final angular velocity and the angular acceleration (assume constant). rpm stands for “revolutions per minute” – we can treat the first part of this problem just like a unit conversion: sec rad 7 . 104 sec 60 min 1 rev 1 rad 2 min 1 rev 1000 = ⋅ π ⋅ Standard units for angular velocity are radians per second This is the Greek letter alpha (looks kinda like a fish) Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB θ r x = rθ Definitions of angular velocity and angular acceleration are analogous to what we had for linear motion. Angular Velocity = ω = t ∆ θ ∆ Angular Acceleration = α = t ∆ ϖ ∆ This is the Greek letter omega (not w) Example: A centrifuge starts from rest and spins for 7 seconds until it reaches 1000 rpm. Find the final angular velocity and the angular acceleration (assume constant). rpm stands for “revolutions per minute” – we can treat the first part of this problem just like a unit conversion: sec rad 7 . 104 sec 60 min 1 rev 1 rad 2 min 1 rev 1000 = ⋅ π ⋅ Standard units for angular velocity are radians per second Now we can use the definition of angular acceleration: 2 sec rad sec rad 15 sec 7 7 . 104 t = = ∆ ϖ ∆ = α Standard units for angular acceleration are radians per second squared....
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 Spring '07
 STANEK
 Physics, Vince Zaccone, Campus Learning, Assistance Services

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