Answer to Question #4848 in Mechanics | Relativity for Chalani Jayawardena

Question

A toy motor car goes two rounds a second in a cicular way that has 0.3m rad.Find the angular velocity,periodic time and the speed of the car.
If the car goes in a circular way that has a 0.4m rad with a 2ms-1 velocity, find the velocity of the car

Answer 1

A toy motor car goes two rounds a time T=1s in a cicular way that has R=0.3m rad. Find the angular velocity, periodic time and the speed of the car.

One round has measure 2pi. So, angular velocity of a car is Va = 2*2pi/1 = 2 rad/s (1rad=2pi).
Car goes N=2 rounds in a one second, so periodic time is 1/2 = 0.5 s.
The length of a round is L = 2pi*R = 2*3.14*0.3 = 1.884 m. So, speed of the car is V = L/T = 2*L/T = 2*1.884/1 = 3,768 m/s.

If the car goes in a circular way that has a 0.4m rad with a V=2 m/s velocity, find the angular velocity of the car

The length of a round is L = 2pi*R = 2*3.14*0.4 = 2,512 m. So, it takes t = L/V = 2,512/2 = 1,256 s to make a round. The angular velocity is a value inverse to a round time, so Va = 1/t = 1/1.256 = 0,796 rad/s.