Help please.....

Question

1) A new car being tested on a circular test track. The track had a radios of 1.2 km.

If the car is moving a constant speed of 14 m s-1 then.

A) How far around the track will the car have gone in 60 s?

B) what is the change in angular displacement in this period of 60 s?

C) What is the angular velocity of the car?

D) how long will it take to complete one lap?

The car doubles its speed from 14m s-1 to 28 m s -1

2) A car is traveling around a circular race track at 180 km h-1. If a single lap of the track is 2.4 km long, what is the angular velocity of the car (in rad s-1)?

Answer 1

Liya

a) Distance = speed x time = 60 x 14 = 840 m

b) Radius of the track is 1.2 km = 1.2 x 1000m = 1200 m

Circumference of the track = 2πr = 2400π m

So in 60s, number of revolutions = 840 / (2400π)

1 revolution = 2π radians

So the angular displacement in 60s will be 840 x 2π / (2400π) radians = 0.7 radians

(c) angular velocity = angular displacement / time = 0.7 / 60 radians per second = 7/600 radians per second (leave it as a fraction)

(d) Time = circumference / speed = 2400π / 14 seconds

(2) 180 km / h = 180 000 m / h = 180000 / 3600 m/s = 50 m/s

r = 2.4 km = 2400 m

So in 1 s, car travels 50m = 50 / (4800π) revolutions = 50 x 2 x π / (4800π) radians = (100/4800) radians = (1/48) radians

So angular velocity is (1/48) radians per second

Mike