A pulley's angular acceleration α is recorded by a blinking sensor around the pulley. Given the data from this sensor...a) Calculate the linear acceleration a. (Hint: u = ωRpulley where Rpulley is 2.5 cm)b) Use the value obtained from part a and get an estimate for the disk’s moment of inertia from I = (mr2)(g−a)/ac) Compare the value obtained from part bto the (MdiskR2disk)/2 which is the moment of inertia of a disk rotating from its center Mdisk = 1.42 kg Spinning disk of 12 cmradits and mass 1.42 gMasslesslleySpindle of 1.5/cmradius100 gr Run #1 (time pt 1) Run #1 (speed pt 1)Time (s)Run #1 (time pt 2) Run #1 (speed pt 2)Angular Speed (rad/s)Angular Speed (rad/s) Time (s)1.5191.35.7145.331.9451.75.8315.442.2875.9455.572.5812.286.0575.682.8422.556.1675.773.0782.786.2755.813.2972.986.3825.953.5013.186.4866.143.6933.366.5876.243.8763.526.6886.34.053.726.7866.44.2153.96.8846.464.3734.056.986.734.5244.237.0746.544.6714.337.1696.744.8154.437.2626.794.9544.557.3536.935.094.717.4437.085.2224.857.5317.275.3495.037.6167.425.4735.17.7017.345.5955.2

Given that: RPulley=2.5 cm=0.025 mm=100 g= 0.1 kgMdisk=1.42 kgRdisk=12 cm=0.12 mr=1.5 cm=0.015 m

Answered: A pulley's angular acceleration α is…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter13: Rotation Ii: A Conservation Approach

Section: Chapter Questions

Problem 71PQ: A long, thin rod of mass m = 5.00 kg and length = 1.20 m rotates around an axis perpendicular to...

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A pulley's angular acceleration α is recorded by a blinking sensor around the pulley. Given the data from this sensor...

a) Calculate the linear acceleration a. (Hint: u = ωR_pulley where R_pulley is 2.5 cm)

b) Use the value obtained from part a and get an estimate for the disk’s moment of inertia from I = (mr²)(g−a)/a

c) Compare the value obtained from part bto the (M_diskR²_disk)/2 which is the moment of inertia of a disk rotating from its center M_disk= 1.42 kg

Spinning disk of 12 cm
radits and mass 1.42 g
Massless
lley
Spindle of 1.5/cm
radius
100 gr

Run #1 (time pt 1) Run #1 (speed pt 1)
Time (s)
Run #1 (time pt 2) Run #1 (speed pt 2)
Angular Speed (rad/s)
Angular Speed (rad/s) Time (s)
1.519
1.3
5.714
5.33
1.945
1.7
5.831
5.44
2.287
5.945
5.57
2.581
2.28
6.057
5.68
2.842
2.55
6.167
5.77
3.078
2.78
6.275
5.81
3.297
2.98
6.382
5.95
3.501
3.18
6.486
6.14
3.693
3.36
6.587
6.24
3.876
3.52
6.688
6.3
4.05
3.72
6.786
6.4
4.215
3.9
6.884
6.46
4.373
4.05
6.98
6.73
4.524
4.23
7.074
6.54
4.671
4.33
7.169
6.74
4.815
4.43
7.262
6.79
4.954
4.55
7.353
6.93
5.09
4.71
7.443
7.08
5.222
4.85
7.531
7.27
5.349
5.03
7.616
7.42
5.473
5.1
7.701
7.34
5.595
5.2

Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .

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