A 30.0 kg wheel, essentially a thin hoop with radius 0.620 m, is rotating at 202 rev/min. It must be brought to a stop in 26.0 s. (a) How much work must be done to stop it? (b) What is the required average power? Give absolute values for both parts.

(a) 2579.99 J.

(b) 99.23 W

Explanation:

(a)

The work done  by the wheel = Kinetic energy of the wheel.

W = 1/2mv² Equation 1

Where W = work done, m = mass of the wheel, v = velocity of the wheel.

But,

v = rω Equation 2

Where r = radius of the wheel, ω = angular velocity

Substitute equation 2 into equation 1

W = 1/2mr²ω² Equation 3

Given: m = 30 kg, r = 0.620 m, ω = 202 rev/min = (202×0.10472) rad/s = 21.153 rad/s

Substitute into equation 3

W = 1/2(30)(0.62²)(21.153²)

W = 2579.99 J.

(b)

Power = work done/time

P = W/t Equation 4

where P = power, W = work done, t = time

Given: W = 2579.99 J, t = 26 s

Substitute into equation 4

P = 2579.99/26

P = 99.23 W.

sleep paralysis is a parasomnia, events associated with sleep.

sleep paralysis happens when you are in the middle of waking up or falling asleep. it is the feeling of being conscious but unable to move. it definitely involves hallucinations.

i had a friend that had sleep paralysis and he told me a story one time where he was laying in bed and he couldn't move his body no matter how hard he tried and there was someone standing in the corner of his room coming towards him. he couldn't move and you can't "wake up" because you are already conscious. sometimes sleep paralysis can be triggered by frequent waking up during the night based off of multiple trips to the bathroom, or if you had ever been abused, sleep paralysis can start happening from things like that.

no. dot product   =0 when vecs at right angles