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Chapter 4: Q. 23 (page 106)

23. FIGURE EX4.23 shows the angular-velocity-versus-time graph for a particle moving in a circle. How many revolutions does the object make during the first 4s

Short Answer

Expert verified

The number if revolution made by the object during first 4s is 10.34rev.

Step by step solution

01

. Given information

The graph is drawn between angular velocity versus time for a particle.

The following graph shows the graph of angular velocity versus time of a particle for first 4s.

02

Step 2. Explanation

The formula to calculate the area of ABC is,

AOABC=OA脳AB

The formula to calculate the area of BCE is,

ABCE=12(CE)(BC)

The formula to calculate the area of DEF is,

ADEF=12(DF)(EF)

The angular displacement of the particle in first from the shown figure (I) is,

胃=AOABC+ABCE+ADEF胃=(OA脳AB)+12(CE)(BC)+12(DF)(EF)胃=((20rad/s)脳(2s))+12(2s)(20rad/s)+12(1s)(10rad/s)=40rad+20rad+5rad=65rad脳1rev2蟺rad=10.34rev

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