Notes. Displacement, Velocity, and Acceleration. Displacement, Velocity, and Acceleration. *Angular* Displacement, Velocity, and Acceleration

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1 Displacement, Velocity, and Acceleration (WHERE and WHEN?) I m not going to teach you anything today that you don t already know! (basically) Practice: 7.1, 7.5, 7.7, 7.9, 7.11, 7.13 Notes Thanks for your feedback! I will state clicker answers clearly. Remind me if I don t! I will try to write bigger on light board! If things are still too small, please do me and you a favor and speak up during class! There will be zero people mad at you. Displacement, Velocity, and Acceleration (WHERE and WHEN?) *Angular* Displacement, Velocity, and Acceleration (WHERE and WHEN?)

2 What you ll be doing Unit conversion (degrees, radians, revs). Angular position, velocity, acceleration. Convert between angular and linear quantities. Linear motion Angular motion Displacement, Velocity, v ω Angular velocity Acceleration, a α Angular acceleration Angular displacement v = v0 + at ω = ω0 + αt at = ωt + ½ αt v = v0 + a ω = ω0 + α = v0t + ½ Units of θ 1 full spin is θ = 360 Degrees θ = π Radians θ = 1 Revolutions (revs) Units of θ 1 half spin is θ = 180 Degrees θ = π Radians θ = 0.5 Revolutions (revs)

3 Let s convert Degrees to radians π radians 360 ( ) = π radians 360 Q67 Your friend wants π/3 radians of pizza. How many degrees is this? A. 30 B. 60 C. 90 D. 10 E. 40 Angular displacement = θf - θi θi = 40 o x Just like we could define initial and final positions, to find linear displacement, we can do the same for angular displacement. Angular displacement = θf - θi θf = 85 o θi = 40 o x Just like we could define initial and final positions, to find linear displacement, we can do the same for angular displacement. Angular displacement θf = 85 o Note: We do NOT treat angular displacement = θf - θi as a vector! θi = 40 o x Just like we could define initial and final positions, to find linear displacement, we can do the same for angular displacement.

4 Average angular velocity Change in rotational angle over time! ω= units: rad/s Just like we could define velocity as displacement over time, we can do the same for angular velocity. What is Earth s angular speed? ω= Remember there are π radians in a full rotation. A. 1 rad/s B. π rad/s C. 3.14e-5 rad/s D. 7.7e-5 rad/s Q68 Average angular acceleration Change in spin rate over time! α= ωf - ωi ω = units: rad/s Just like we could define acceleration as change in velocity over time, we can do the same for angular acceleration. Same process as kinematics: List what you know in variable form, then match with a formula Linear v= a= v Rotational ω= α= ω e lin e! he erag t te: av No ans e m For constant a: For constant α: v = vo + at ω = ω o + αt = vot + 1 at = ωot + 1 αt v = vo + a ω = ω o + α

5 Q69 BIG BEN in London and a tiny alarm clock both keep perfect time. Which minute hand has the bigger angular velocity ω? ω = θ A. Big Ben B. Little alarm clock C. Both have the same ω = Arc length r = Radius r = r = Arc length r = Radius = r r What is for one rotation (circumference of a circle)? A.πr B. πr C.πr D.πr Q70

6 CAREFUL! The tires on a car have a diameter of 0.5 m and are warrantied for 100,000 km. Determine the angle (in radians) through which one of these tires will rotate during the warranty period. = r How many revolutions of the tire are equivalent to our answer? v is linear speed of point P Linear to angular velocity v = rω Bigger v Smaller v

7 If you re standing at the equator, what is your linear speed with respect to the Earth s center? (Earth s radius is ~ 6400 km.) v = rω = r v = r ω a = r α Q71 chalk Kids tricycle I put stickers on the bottom of the front and back wheels of different sizes. As I roll this tricycle (without slipping), the stickers complete a circle (360 degrees) at: A. The same time B. Different times C. Depends on the speed of the bike v = r ω Linear v = v a = For constant a: Rotational ω = θ α = ω For constant α: v = v + o at ω = ω t o + α = v t 1 o + at v = vo + a Same process as kinematics: List what you know in variable form, then match with a formula Note the line means average! = ω o t + α 1 t ω = ω o + α = r v = rω a = rα

8 To throw a curve ball, a pitcher gives the ball an initial angular speed of 36.0 rad/s. When the catcher gloves the ball s later, its angular speed has decreased (due to air resistance) to 34. rad/s. (a) What is the ball s angular acceleration, assuming it to be constant? (b) How many revolutions does the ball make before being caught? ω = θ α = ω ω = ω o + αt = ω o t + α 1 t ω = ω o + α Have a great spring break!