Answer:
a) tires rubbing, b) the weight has a component parallel to the floor
c) he child's back support, d) The tension of the rope and weight
Explanation:
In this exercise, we are asked to indicate the origin of the forces for the centripetal movement parallel to the rope, e) gravitational force
a) When a car turns, the centripetal force has two origins
* The tires rubbing against the road
* If the road has a lean angle, the component of the weight directed towards the center of the circle also contributes to the centripetal force.
b) the child in general has some degree of inclination with respect to the post, for which the weight has a component parallel to the floor that is responsible for the centripetal movement of the system
c) The bench rotates together with the carousel, so the child's back support is the response to the centripetal force
d) The tension of the rope has two components: the component perpendicular to the movement and the component of the weight (parallel to the rope) the difference of these two forces is the centripetal force
e) The gravitational force of the sun on the earth is what creates the centripetal motion
<span>If it stopped spinning completely, you would get 1/2 year daylight and 1/2 year nightime!! During daytime for 6 months, the surface temperature would depend on your latitude, being far hotter that it is now at the equator than at the poles where the light rays are more slanted and heating efficiency is lower. This long-term temperature gradient would alter the atmospheric wind circulation pattern so that the air would move from the equator to the poles rather than in wind systems parallel to the equator like they are now!</span>
Answer:
The time is 16 min.
Explanation:
Given that,
Time = 120 sec
We need to calculate the moment of inertia
Using formula of moment of inertia
![I=\dfrac{1}{2}MR^2](https://tex.z-dn.net/?f=I%3D%5Cdfrac%7B1%7D%7B2%7DMR%5E2)
If the disk had twice the radius and twice the mass
The new moment of inertia
![I'=\dfrac{1}{2}\times2M\times(2R)^2](https://tex.z-dn.net/?f=I%27%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes2M%5Ctimes%282R%29%5E2)
![I'=8I](https://tex.z-dn.net/?f=I%27%3D8I)
We know,
The torque is
![\tau=F\times R](https://tex.z-dn.net/?f=%5Ctau%3DF%5Ctimes%20R)
We need to calculate the initial rotation acceleration
Using formula of acceleration
![\alpha=\dfrac{\tau}{I}](https://tex.z-dn.net/?f=%5Calpha%3D%5Cdfrac%7B%5Ctau%7D%7BI%7D)
Put the value in to the formula
![\alpha=\dfrac{F\times R}{\dfrac{1}{2}MR^2}](https://tex.z-dn.net/?f=%5Calpha%3D%5Cdfrac%7BF%5Ctimes%20R%7D%7B%5Cdfrac%7B1%7D%7B2%7DMR%5E2%7D)
![\alpha=\dfrac{2F}{MR}](https://tex.z-dn.net/?f=%5Calpha%3D%5Cdfrac%7B2F%7D%7BMR%7D)
We need to calculate the new rotation acceleration
Using formula of acceleration
![\alpha'=\dfrac{\tau}{I'}](https://tex.z-dn.net/?f=%5Calpha%27%3D%5Cdfrac%7B%5Ctau%7D%7BI%27%7D)
Put the value in to the formula
![\alpha=\dfrac{F\times R}{8\times\dfrac{1}{2}MR^2}](https://tex.z-dn.net/?f=%5Calpha%3D%5Cdfrac%7BF%5Ctimes%20R%7D%7B8%5Ctimes%5Cdfrac%7B1%7D%7B2%7DMR%5E2%7D)
![\alpha=\dfrac{2F}{8MR}](https://tex.z-dn.net/?f=%5Calpha%3D%5Cdfrac%7B2F%7D%7B8MR%7D)
![\alpha=\dfrac{\alpha}{8}](https://tex.z-dn.net/?f=%5Calpha%3D%5Cdfrac%7B%5Calpha%7D%7B8%7D)
Rotation speed is same.
We need to calculate the time
Using formula angular velocity
![\Omega=\omega'](https://tex.z-dn.net/?f=%5COmega%3D%5Comega%27)
![\alpha\time t=\alpha'\times t'](https://tex.z-dn.net/?f=%5Calpha%5Ctime%20t%3D%5Calpha%27%5Ctimes%20t%27)
Put the value into the formula
![\alpha\times120=\dfrac{\alpha}{8}\times t'](https://tex.z-dn.net/?f=%5Calpha%5Ctimes120%3D%5Cdfrac%7B%5Calpha%7D%7B8%7D%5Ctimes%20t%27)
![t'=960\ sec](https://tex.z-dn.net/?f=t%27%3D960%5C%20sec)
![t'=16\ min](https://tex.z-dn.net/?f=t%27%3D16%5C%20min)
Hence, The time is 16 min.