Cambridge International AS and A level Physics
i
cos 1.0
ii tan 1.0 iii sin 0.10 ⎛ π⎞
iv sin ⎜ ⎟ ⎝ 4⎠ ⎛π ⎞
v cos ⎜ ⎟ ⎝3 ⎠ Your calculator is likely to have a π key. c Determine the following angles; give your answers in radians and to three significant figures: i
sin−1 0.50
ii cos −1 (−0.65).
Exercise 17.2 Uniform circular motion An object that moves around a circular path at a steady speed is described as having uniform circular motion. This is an exercise to develop understanding of the relationships between velocity, angular velocity, period, angle and radius. 1 A fairground ride consists of several cars travelling around on a vertical wheel of radius r = 20.0 m. Each car makes one complete circuit in a time T = 35 s. a During each circuit, a car travels around 360°. This is its angular displacement θ. Give the value of θ in radians. 108
b Calculate the car’s angular velocity ω. c Calculate the distance travelled by the car during one circuit (= 2πr). d Calculate the car’s speed v using speed =
distance . time
e Calculate the car’s speed using v = rω. Check that your answers to d and e are the same. 2 Two runners, A and B, are jogging side by side around a circular running track. a Runner A jogs along the centre of the track. Here, the radius of the track is 100.0 m. Calculate the distance travelled in one complete circuit. (Give your answer to one decimal place.) b Runner B jogs beside runner A, at a distance of 0.80 m further from the centre of the track. How much further does B travel than A when completing a circuit? c Runner A runs at a steady speed of 5.0 m s−1. Determine the speed at which B must run in order to stay beside runner A. 3 A train moves along a curved section of track at a steady speed of 18.0 m s−1. a The curved section of track has a length of 900 m. Deduce how long it will take the train to travel this distance. b The radius of curvature of the track is 3.60 km. Calculate the angle through which the train has moved (its angular displacement). Remember: angle in radians = c Calculate the angular velocity of the train.
length of arc radius
d Draw a diagram to show the curved section of the track. Add arrows to show the velocity of the train at the start of the section and at the end.