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?)
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)
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.
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
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
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
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
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 0.595 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!