When we use angle to describe the position of an we can the same to describe the

Question

When we use angle to describe the position of an we can the same to describe the angular velocity (w) of its rotation. The definition for linear velocity is change in position divided by change in time. Angular velocity is the same, but it is change in angular position divided by change in time as seen on the right. object, do thing 1) Calculate the angular velocity (), the period (T), and the frequency (f) for a rotating disc in the following situations: a) The disc rotates 360 degrees in 1 second b) The disc rotates 2 radians in 1 second c) The disc rotates radians in 1 second d) The disc rotates 2 radians in 7 seconds e) The disc disc rotate 5/2 radians in 10 seconds

Explanation / Answer

a)

o=360*(pi/180)=2pi radians

angular velocity

W=2pi/1 =6.28 rad/sec

Period

T=2pi/W =2pi/6.28 =1 s

frequency

f=1/T =1/1 =1 Hz

b)

angular velocity

W=2pi/1 =6.28 rad/sec

Period

T=2pi/W =2pi/6.28 =1 s

frequency

f=1/T =1/1 =1 Hz

c)

angular velocity

W=pi/1 =3.14 rad/sec

Period

T=2pi/3.14 =2

frequency

f=1/T =1/2 =0.5 Hz

d)

angular velocity

W=2pi/7 =0.8976 rad/sec

Period

T=2pi/0.8976=7 s

frequency

f=1/T =1/7 =0.143 Hz

e)

angular velocity

W=(5/2pi)/10 =0.08 rad/sec

Period

T=2pi/0.08 =79 s

frequency

f=1/T =1/79 =0.01267 Hz

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