Answer:
α(0) = 0 rad/s²
α(5) = 15 rad/s²
Explanation:
The angular velocity of the flywheel is given as follows:
w(t) = A + B t²
where, A and B are constants.
Now, for the angular acceleration, we must take derivative of angular velocity with respect to time:
Angular Acceleration = α (t) = dw/dt
α(t) = (d/dt)(A + B t²)
α(t) = 2 B t
where,
B = 1.5
<u>AT t = 0 s</u>
α(0) = 2(1.5)(0)
<u>α(0) = 0 rad/s²</u>
<u></u>
<u>AT t = 5 s</u>
α(5) = 2(1.5)(5)
<u>α(5) = 15 rad/s²</u>
Pressing two objects together with more force Increase friction
The mass of an object has no effect whatsoever on the object's
acceleration during free-fall. If there is no air resistance to interfere
with the natural effects of gravity, then a feather and a battleship ...
dropped at the same time ... fall together, and hit the ground at the
same time.
Answer:
Centripetal Acceleration 18.75 m/s^2, Rotational Kinetic Energy 843.75 J
Explanation:
a Linear acceleration (we cant find tangential acceleration with the givens so we will find centripetal)
a= ω^2*r
ω= 300rev/min
convert into rev/s
300/60= 5rev/s
a= 18.75m/s^2
b) use Krot= 1/2 Iω^2
plug in gives
1/2(30*2.25)(25)= 843.75 J
(a) This is a freefall problem in disguise - when the ball returns to its original position, it will be going at the same speed but in the opposite direction. So the ball's final velocity is the negative of its initial velocity.
Recall that
We have 
, so that
(b) The speed of the ball at the start and at the end of the roll are the same 8 m/s, so the average speed is also 8 m/s.
(c) The ball's average velocity is 0. Average velocity is given by 
, and we know that .
(d) The position of the ball 
at time 
is given by
Take the starting position to be the origin, 
. Then after 6 seconds,
so the ball is 42 m away from where it started.
We're not asked to say in which direction it's moving at this point, but just out of curiosity we can determine that too:
Since the velocity is positive, the ball is still moving up the incline.
