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Romashka [77]
3 years ago
5

A uniform disk with radius 0.650 m

Physics
1 answer:
VashaNatasha [74]3 years ago
3 0

Answer:

a = 13.758\,\frac{m}{s^{2}}

Explanation:

First, the instant associated to the angular displacement is:

(1.10\,\frac{rad}{s} )\cdot t + (6.30\,\frac{rad}{s^{3}} )\cdot t^{2} - 0.628\,rad = 0

Roots of the second-order polynomial are:

t_{1} \approx 0.240\,s, t_{2} \approx -0.415\,s

Only the first root is physically reasonable.

The angular velocity is obtained by deriving the angular displacement function:

\omega (0.240\,s) = 1.10\,\frac{rad}{s}+ (12.6\,\frac{rad}{s^{2}})\cdot (0.240\,s)

\omega (0.240\,s) = 4.124\,\frac{rad}{s}

The angular acceleration is obtained by deriving the previous function:

\alpha (0.240\,s) = 12.6\,\frac{rad}{s^{2}}

The resultant linear acceleration on the rim of the disk is:

a_{t} = (0.650\,m)\cdot (12.6\,\frac{rad}{s^{2}} )

a_{t} = 8.190\,\frac{m}{s^{2}}

a_{n} = (0.650\,m)\cdot (4.124\,\frac{rad}{s} )^{2}

a_{n} = 11.055\,\frac{m}{s^{2}}

a = \sqrt{a_{t}^{2}+a_{n}^{2}}

a = 13.758\,\frac{m}{s^{2}}

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