The driver of a car sets the cruise control and ties the steering wheel so that the car travels at a uniform speed of in a circle with a diameter of 120 m. a) through what angular distance does the car move in 4.00 min? b) what linear distance does it travel in this time?

Answer

given,                                  

diameter of the circle = 120 m

time  =4 min = 4 × 60 = 240 s

linear velocity be = 15 m/s

we know                      

v = r ω                          

ω =

ω =

ω = 0.25 rad/s

angular distance in time 4 min

d = ω t                                      

d = 0.25 × 240                          

d = 60 radian              

b) linear distance          

d = s × t                  

d = 15 × 240

d = 3600 m

(a) Angular distance is 4v m

(b) Linear distance is 240 v m

Solution:

As per the question:

Let the uniform speed of the car be 'v' m/s

Diameter of the car, D = 120 m

Radius of the car, r = 60 m

Time, t = 4.00 min = 240 s

Now,

(a) The angular speed of the car is given by:

rad/s

Now, the angular displacement is given by:

m

(b) The linear distance, d is given by:

d = vt = 240v m

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