Question #294234

A ball rolls up in an inclined plane with an initial angular velocity 100



(a) if its radius is r. What is it initial linear velocity? After the time t the ball stops.



(b) what is it angular retardation



(C) what is the angular displacement before its stops

1
Expert's answer
2022-02-06T14:34:11-0500

Explanations and Calculations


a)

  • Initial linear velocity is V=rω=100r\small V=r\omega=100r


b)

  • If the angular retardation is α\small \alpha ,

ωf=ωi+α.tα=0100t=100t\qquad\qquad \begin{aligned} \small \omega_f&=\small \omega_i+\alpha.t\\ \small \alpha&=\small \frac{0-100}{t}\\ &=\small -\frac{100}{t} \end{aligned}

c)

  • If the angular displacement is θ,\small \theta,

θ=ω.t+12αt2=100t12×100t×t2=100t50t=50t\qquad\qquad \begin{aligned} \small \theta&=\small \omega.t+\frac{1}{2} \alpha t^2\\ &=\small 100t-\frac{1}{2}\times\frac{100}{t}\times t^2\\ &=\small 100t-50t\\ &=\small 50t \end{aligned}

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