1. A disk spinning at 25 rad/s experiences a constant angular acceleration of 5.

Question

1. A disk spinning at 25 rad/s experiences a constant angular acceleration of 5.0 rad/s2. (Show all work!!!)

a) What will the disk’s angular speed equal after 8.0 s of this acceleration?

b) Through how many radians will the disk rotate in 8.0 s?

c) What constant acceleration will cause the disk to stop spinning in 2.0 s from its speed of part a)?

d) Assume the disk’s moment of inertia is 0.010 kgm2. What net torque will cause the disk to stop?

e) I = ½ m R2. Assume the disk’s radius is 0.050 m. Calculate its mass.

Explanation / Answer

(a)  disk’s angular speed w = w0 + a*t

= (25 + 5.0*8.0) rad/s

= 65 rad/s

(b) rotated angle = w0*t + (1/2)*a*t^2

= (25*8.0 + 0.5*5.0*64) rad

= (200 + 160) rad

= 360 rad

(c) let a is the constant acceleration

then 0 = 65 + 2.0*a

a= -32.5 rad/s^2

(d) net torque = I*a = 0.010*32.5 = 0.00325 N-m

(e) I = (1/2)*m*R^2

m = 2*I/R^2 = 2*0.010/0.050^2 kg = 8kg

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