In a department store toy display, a small disk (disk 1) of radius 0.100 m is dr

Question

In a department store toy display, a small disk (disk 1)
of radius 0.100 m is driven
by a motor and turns a larger
disk (disk 2) of radius 0.500 m.
Disk 2, in turn, drives disk 3,
whose radius is 1.00 m. The
three disks are in contact,
and there is no slipping.
Disk 3 is observed to sweep
through one complete revolution every 30.0 s.
a) What is the angular speed of disk 3?
b) What is the ratio of the tangential velocities of the rims
of the three disks?
c) What is the angular speed of disks 1 and 2?
d) If the motor malfunctions, resulting in an angular
acceleration of 0.100 rad/s2 for disk 1, what are disks 2 and
3’s angular accelerations?

Explanation / Answer

a)
3 = 2**f = 2*3.14*(1/30) = 0.209 rad/s

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b)

S1 = S2 = S3 >>>>> V1 = V2 =V3

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c)

V1 = V3 >>>> R1 * 1 = R3 * 3

>>>> 1 = (R3/R1)*3 = (1/0.1)*0.209

>>>> 1 = 2.09 rad/s

V2 = V3 >>>> R2 * 2 = R3 * 3

>>>> 2 = (R3/R2)*3 = (1/0.5)*0.209

>>>> 2 = 0.418 rad/s

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d)

a1 = a2 = a3 >>>> R1 * 1 = R2 * 2 = R3 * 3

>>>>> 1 = (R3/R1) * 3 = (1/0.1)*0.1

>>>>> 1 = 1 rad/s2

>>>>> 2 = (R3/R2) * 3 = (1/0.5)*0.1

>>>>> 2 = 0.2 rad/s2

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