Cicula motion Objectives Descibe the acceleated motion of objects moving in cicles. Use equations to analyze the acceleated motion of objects moving in cicles.. Descibe in you own wods what this equation means: Physics tems angula velocity adian 2. A bicycle moves with a speed of 30 km/h. If the wheels of the bicycle have a adius of 30 cm, what is the angula velocity of the wheels? Give you answe in adians/second. Equations Cicula motion A tuning wheel, a spinning top and the Eath obiting the Sun ae all examples of cicula motion. Just like objects moving in staight lines, objects in cicula motion have position, velocity and acceleation.
Linea velocity If you whil a yo-yo in a cicle ove you head at a constant ate, how can you figue out its speed? Linea velocity If you whil a yo-yo in a cicle ove you head at a constant ate, how can you figue out its speed? What distance d do you need to know? Linea velocity If you whil a yo-yo in a cicle ove you head at a constant ate, how can you figue out its speed? Linea velocity What time t do you need to know? What distance d do you need to know? the cicumfeence: Linea velocity Linea velocity What time t do you need to know? Fo an object moving in unifom cicula motion, its speed is: the time it takes go once aound the cicle: What is the diection of the velocity vecto? Can you descibe it? This called the peiod, T. 2
Linea velocity Fo an object moving in unifom cicula motion, its speed is: Test you knowledge A Feis wheel at the fai otates once evey 0 seconds, and has a adius of 7.0 m. What is the speed its ides? What is the diection of the velocity vecto? Can you descibe it? The velocity vecto is always tangent to the cicle and pependicula to the adius vecto. v v Test you knowledge A Feis wheel at the fai otates once evey 0 seconds, and has a adius of 7.0 m. What is the speed its ides? Angula velocity You can also use angle measues to descibe cicula motion. Position in cicula motion is given by an angle. The Geek lette θ is used to epesent angles. v Angula velocity The ate at which a otating object spins is called angula velocity (ω). Angula velocity The ate at which a otating object spins is called angula velocity (ω). If θ is measued in adians, ω is in adians/second. 3
Angula velocity The ate at which a otating object spins is called angula velocity (ω). What is a adian? How many adius lengths does it takes to cove the full cicumfeence of any cicle? If θ is measued in adians, ω is in adians/second. But what is a adian? What is a adian? How many adius lengths does it takes to cove the full cicumfeence of any cicle? 3 2 What is a adian? One adian is the angle fomed by wapping one adius of length aound the cicumfeence of a cicle. Thee ae 2π adians in a full cicle. The cicumfeence equals 2π adii: C = 2π 6.28 4 6 Take a guess: How many degees do you think is in one adian? 5 What is a adian? One adian equals about 57.3 One adian is equal to this atio: Units fo angula velocity Angula velocity has units of adians pe second. An object that makes one complete otation each second has an angula velocity of... 4
Exploing the ideas Click this inteactive calculato on page 208. What is a wheel's angula velocity if it otates by 57.3 evey second? ( adian= 57.3 ) Angula velocity What is a wheel's angula velocity if it otates by 57.3 evey second? What is a wheel's angula velocity if it otates though six complete tuns in two seconds? 37.7 2 Angula velocity Angula velocity Click [Run] to obseve the motion. Othe units fo angula velocity What is a wheel's angula velocity if it otates though six complete tuns in two seconds? 8.8 37.7 Othe ways to expess the units fo angula velocity: adians pe second degees pe second cycles pe second OR evolutions pe minute (pm) How can you make a negative angula velocity? Angula velocity 2 Click [Run] to obseve the motion. An object making one complete otation each second has an angula velocity of... 5
Test you knowledge The Eath otates once evey 24 hous. What is its angula velocity in adians pe second? Test you knowledge The Eath otates once evey 24 hous. What is its angula velocity in adians pe second? Hint: Fist, convet hous to seconds. Test you knowledge The Eath otates once evey 24 hous. What is its angula velocity in adians pe second? Rolling wheels A olling wheel is moving fowad AND spinning. It has linea AND angula velocity. These two velocities ae elated by geomety. Rolling wheels linea velocity: Rolling wheels linea velocity: angula velocity: 6
Rolling wheels Old bicycles linea velocity: angula velocity: The lage the adius of a bicycle wheel, the highe the linea velocity of the bike. theefoe: Old bicycles Old bicycles The lage the adius of a bicycle wheel, the highe the linea velocity of the bike. Poblem: Lage wheels make bicycles fast, but unstable. The lage the adius of a bicycle wheel, the highe the linea velocity of the bike. Poblem: Lage wheels make bicycles fast, but unstable. Solution: Moden bicycles uses geas and chains so that the pedals can tun at a diffeent angula velocity than the wheels. Exploing the ideas The wheels on a coveed wagon ae.6 mete in diamete, and tun once evey two seconds. Click the inteactive calculato on page 209 a) What is ω? b) How fast is the wagon taveling? 0 0 Linea velocity 7
The wheels on a coveed wagon ae.6 mete in diamete, and tun once evey two seconds. You bicycle has wheels with a adius of 30 cm. As you ide, the wheels spin aound five times each second. a) What is ω? Linea velocity a) What is ω? Linea velocity 3.4 3.4 0.80 0 0.30 b) How fast is the wagon taveling? Click [Run] to obseve the motion. b) How fast ae you iding? You bicycle has wheels with a adius of 30 cm. As you ide, the wheels spin aound five times each second.. Descibe in you own wods what this equation means: a) What is ω? Linea velocity 9.4 3.4 0.30 b) How fast ae you going? Click [Run] to obseve the motion.. Descibe in you own wods what this equation means: 2. A bicycle moves with a speed of 30 km/h. If the wheels of the bicycle have a adius of 30 cm, what is the angula velocity of the wheels? Give you answe in adians/second. This is the equation fo angula velocity. It measues the ate at which an object otates. The angula velocity equals the angle Δθ (in adians) though which the object tuns, divided by the elapsed time Δt. 8
2. A bicycle moves with a speed of 30 km/h. If the wheels of the bicycle have a adius of 30 cm, what is the angula velocity of the wheels? Give you answe in adians/second. Asked: ω Given: v, convet velocity to m/s: 2. A bicycle moves with a speed of 30 km/h. If the wheels of the bicycle have a adius of 30 cm, what is the angula velocity of the wheels? Give you answe in adians/second. Asked: ω Given: v, convet velocity to m/s: Relationship: Solution: 9