A uniform-density wheel of mass 9 kg and radius 0.40 m rotates on a low-friction axle. Starting from rest, a string wrapped around the edge exerts a constant force of 13 N for 0.72 s. (a) What is the final angular speed? Entry field with correct answer 5.2 radians/s (b) What was the average angular speed? Entry field with incorrect answer 1.872 radians/s (c) Through how big an angle did the wheel turn? Entry field with incorrect answer 1.3478 radians/s (d) How much string came off the wheel? Entry field with incorrect answer 0.8469 m

Explanation:

Moment of inertia of wheel = 1/2 x mR²  , m is mass and R is radius of wheel

= .5 x 9 x .4²

= .72 kg m²

Torque created on wheel by string = T x r , T is tension and r is radius of wheel .

13 x .4 = 5.2 N m

angular acceleration α = torque / moment of inertia

= 5.2 / .72

= 7.222 rad /s²

a ) final angular speed = α x t , α is angular acceleration , t is time.

=  7.222  x .72

= 5.2 rad /s

b )

θ = 1/2 α t² , θ  is angle turned , t is time

= .5 x 7.222 x .72²

= 1.872 rad

average angular speed = θ / t

= 1.872 / .72

= 2.6 rad /s

c )

angle turned = 1.872 rad ( discussed above )

d )

length of string coming off

=  angle rotated x radius of wheel

= 1.872 x .4

= .7488 m .

74.88 cm

scientific laws are the result of testing theories and proving them to be facts.

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.