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

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