Question

A sphere and a steel cylinder (? = 7850 kg / m3), both with the same radius ? and mass ? = 1kg,

roll without slipping on an inclined plane at an angle ? = 30 °.

Determine:

a) An expression for the angular velocity \large \boldsymbol{w} (?) given an angular velocity \large \boldsymbol{w} ?. If both systems start from rest, after 7s,

b) What is the angular velocity of the cylinder?

C) What is the angular velocity of the sphere?

Pure rolling analysis.La

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Answer #1

to foriction mesmp mgrosping B. Pure Rolling CRotatás + Translation) Translation ng sinß-fema - 0 Rotation fo R = IQ f. R= MK3-M vam V S. TR= 3 7850 R=0.0317 a = g singo 14 ka 12 g a. 2R(1+1 122 W Wotat gt Wot 28 (1+R?R? given 1-0 t-7 for cylinder gtfor sphere gt co 2R (1+/ 5gt 14 R 589.887 14X0-031 790.3 rad/sec

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