torque, KE, power, angular acceleration question?

Question

A flat grindstone of mass M=1000kg is mounted on a frictionless bearing so it can rotate freely about the vertical axis passing through its center. The grindstone has zero initial angular acceleration and has a radius of .5m. A string is tied around its periphery and is pulled with a constant force of 10N. Find...

a. Find the torque exerted by the string with respect to the center of the grindstone.
b. Find the angular acceleration.
c.Find how much string will have been unwound 10s after the force was initially applied.
d.Find the kinetic energy of the body.
e. Find the amount of power delivered during rotations.

Answer 1

I will assume the grindstone starts from rest, no angular speed.

a) The torque is F*r, or
10*.5=5 N m

b) Angular acceleration is alpha, I will use a
T=I*a
where a is the moment of inertia is
.5*m*r^2
so
5=.5*1000*.5^2*a
a=.04 radians /s^2

c) compute the angular displacement after 10 s
the equation of rotational motion is
th=.5*a*t^2
th=.5*.04*100
th=2 radians

convert radians to distance, multiply the angle by the radius
2*.5 = 1 m

d) The kinetic energy is
.5*I *w^2
where w is the rotational speed
w=a*t
so w=.04*10
w=.4 radians per second
and
KE=.5*.5*1000*.5^2*.4^2

KE=10 J

e) Power, I will assume you are asking for average power to achieve the KE,

=KE/t, or 1 Watt average

j

Answer 2

this is possible to save kinetic means in a flywheel, what you want is a suited transmission. besides the fact that, flywheels can no longer save the equivalent volume of means which would be stored by using chemical storage structures, like batteries, and that they lose the means very rapid simply by air and mechanical friction, so flywheels are used as non everlasting means shops, to point fluctuations in bypass of means, like the flywheel on a vehicle motor. besides the fact that this is possible to transform the flow of gymnastics machines to electrical energy, an consumer-friendly generator and battery device could desire to do it.