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Calculating the Time for a Fishing Reel to Stop Spinning · Physics Playground

Exercícios Movimento circular e gravidade

Exemplo de Physics, 6.3 Rotational Motion

Calculating the Time for a Fishing Reel to Stop Spinning

Problema e solução em inglês, como no livro original.

A deep-sea fisherman uses a fishing rod with a reel of radius 4.50 cm. A big fish takes the bait and swims away from the boat, pulling the fishing line from his fishing reel. As the fishing line unwinds from the reel, the reel spins at an angular velocity of 220 rad/s. The fisherman applies a brake to the spinning reel, creating an angular acceleration of −300 rad/s². How long does it take the reel to come to a stop?

The figure shows an illustration of a fishing reel. The fishing line has an arrow pointing away from the reel with a Linear or translational qualities label pointing to x, v, and a. The radius of the reel to where the string is labeled r=4.5. The Direction of rotation is labeled with an arrow pointing counterclockwise and a Rotational qualities label pointing to theta, omega, and alpha.

Resolva no papel primeiro. Depois abra a solução um passo de cada vez e pare assim que conseguir terminar sozinho.

Estratégia
We are asked to find the time t for the reel to come to a stop. The magnitude of the initial angular velocity is $ω_{0} = 220$ rad/s, and the magnitude of the final angular velocity $ω = 0$ . The signed magnitude of the angular acceleration is $α = - 300$ rad/s², where the minus sign indicates that it acts in the direction opposite to the angular velocity. Looking at the rotational kinematic equations, we see all quantities but t are known in the equation $ω = ω_{0} + α t$ , making it the easiest equation to use for this problem.
Solução
The equation to use is $ω = ω_{0} + α t$ .

We solve the equation algebraically for t, and then insert the known values.

$\begin{matrix} t & = & \frac{ω - ω_{0}}{α} \\ = & \frac{0 - 220 rad/s}{- 300 {rad/s}^{2}} \\ = & 0.733 s \end{matrix}$
6.12

0 de 2 passos abertos

Como foi?

AnteriorFrictional Force on Car Tires Rounding a Curve Próximo Calculating the Torque on a Merry-Go-Round

De Physics (1st edition), da OpenStax (Rice University), seção 6.3, sob licença CC BY 4.0. Original em openstax.org. Dividimos a solução em passos; as palavras, os números e as figuras são do livro. A OpenStax não endossa este site.

Estratégia

Solução