Consider an object moving on a circular path with a radius o

Consider an object moving on a circular path with a radius of 5.7 meters.

How many radians are swept out when the object travels 9.12 meters on the circular path?

__________ radians   

How many meters does the object travel when it sweeps out 141 degrees on the circular path?

__________ meters   

If the object sweeps out 22 radians on the circular path, how many meters has it traveled?

_________ meters   

Suppose the distance the object traveled on the circular path varied from 3.2 meters to 11 meters. How many radians did the object sweep out over this distance?

________ radians

Solution

An object covers 2pi*r m in 360 degree

that is 2*3.14* 5.7 m in 360 degree

so it covers 9.12 m in 360 *9.12/35.796=91.7 degree=91.7*pi/180=.51 radian

b. when moving 2pi*5.7 it completes 360 degree

Therefore 141 degree is completed in 2pi*5.7*141/360=14.02 m

d. change in distance travelled= 11-3.2=7.8 m

In 2*3.14*5.7 it completes 360 degree

Therefore in 7.8 m it completes= 360*7.8/2*3.14*5.7=78.4 degree= 78.4*pi/180radians=.44pi radians