An electric engine turning a workshop sanding rotation at 1.00 × 10² rev/min is switched off. Take the wheel includes a regular negative angular acceleration of volume 2.00 rad/s². 5.25 moments long it takes the grinding rotation to control.
<h3>What is negative angular acceleration?</h3>
- A particle that has a negative angular velocity rotates counterclockwise.
- Negative angular acceleration () is a "push" that is hence counterclockwise.
- The body will speed up or slow down depending on whether and have the same sign (and eventually go in reverse).
- For instance, when an object rotating counterclockwise slows down, acceleration would be negative.
- If a rotating body's angular speed is seen to grow in a clockwise direction and decrease in a counterclockwise direction, it is given a negative sign.
- It is known that a change in the linear acceleration correlates to a change in the linear velocity.
Let t be the time taken to stop.
ω = 0 rad/s
Use the first equation of motion for rotational motion
ω = ωo + α t
0 = 10.5 - 2 x t
t = 5.25 second
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Answer:
![X=X_o+\dfrac{1}{2}gt^2](https://tex.z-dn.net/?f=X%3DX_o%2B%5Cdfrac%7B1%7D%7B2%7Dgt%5E2)
Explanation:
Given that
Length = L
At initial over hanging length = Xo
Lets take the length =X after time t
The velocity of length will become V
Now by energy conservation
![\dfrac{1}{2}mV^2=mg(X-X_o)](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7DmV%5E2%3Dmg%28X-X_o%29)
So
![V=\sqrt{2g(X-X_o)}](https://tex.z-dn.net/?f=V%3D%5Csqrt%7B2g%28X-X_o%29%7D)
We know that
![\dfrac{dX}{dt}=V](https://tex.z-dn.net/?f=%5Cdfrac%7BdX%7D%7Bdt%7D%3DV)
![\dfrac{dX}{dt}=\sqrt{2g(X-X_o)}](https://tex.z-dn.net/?f=%5Cdfrac%7BdX%7D%7Bdt%7D%3D%5Csqrt%7B2g%28X-X_o%29%7D)
![\sqrt{2g}\ dt=(X-X_o)^{-\frac{1}{2}}dX](https://tex.z-dn.net/?f=%5Csqrt%7B2g%7D%5C%20dt%3D%28X-X_o%29%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7DdX)
At t= 0 ,X=Xo
So we can say that
![X=X_o+\dfrac{1}{2}gt^2](https://tex.z-dn.net/?f=X%3DX_o%2B%5Cdfrac%7B1%7D%7B2%7Dgt%5E2)
So the length of cable after time t
![X=X_o+\dfrac{1}{2}gt^2](https://tex.z-dn.net/?f=X%3DX_o%2B%5Cdfrac%7B1%7D%7B2%7Dgt%5E2)
Thus, more than 30 J of potential energy can be loosed by the ball. Thus, the gravitational potential energy of the ball is more than 30 J.
If there is no air resistance, the ball's potential energy is entirely transformed into kinetic energy. When air resistance is taken into account, a portion of the potential energy is used to overcome it. Thus, AU > AKE. In the current scenario, a ball gains 30 J of kinetic energy while falling and is treated as encountering air resistance. The energy that an object retains due to its position in relation to other objects, internal stresses, electric charge, or other factors is known as potential energy in physics. The potential energy will be transformed into kinetic energy if the stones fall. High on the tree, branches have the potential to fall, which gives them energy. Chemical potential energy exists in the food we eat.
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