Question

(Figure 1) shows the angular-velocity-versus-time graph for a particle moving in a circle. How many revolutions does the object make during the first 4 s?

Answer 1

Answer: 10.34

Explanation:

Given

$\omega -t$ graph for a particle is given

angle turned by the particle in radians is given by the area under $\omega -t$ graph

The area is given by

$A=20\times (2-0)+10(4-2)+\dfrac{1}{2}\times (20-10)\times (3-2)\\A=40+20+5=65\ rad$

Revolutions(N) made by the object is given by

$N=\dfrac{65}{2\pi }=10.34$