Problem 4A 9-kg disk has an initial angular rate of wo=+17 rad/s and itscenter of mass has a velocity vo =–7 m/s. The radius of the disk isr = 30 cm, and the coefficient of kinetic friction between thesurface and disk is µk = 0.21.r 21 cmUse the conventions that positive velocities are to the right,negative velocities are to the left, positive angular rates arecounter-clockwise, and negative rates are clockwise in all cases.a. What is an expression, in terms of r, o and v, forthe kinematic condition of rolling without slipping?b. Draw a clear and complete free body diagram of just the disk in the space provided below.c. What is the mass moment of inertia of the disk about its center of mass?d. What is the angular acceleration of the disk?e. What is the linear acceleration of the disk?f. For how much time does the disk slide before it begins to roll without slip?g. What is the velocity of the disk at the instant it begins to roll without slip?h. For how much distance does the disk slide before it begins to roll without slip?Side view FBD

Given data as per question m=9 kgω0=17 radsv0= −7 msr=30 cm=0.3 mμ=0.21…

A 9-kg disk has an initial angular rate of wo = +17 rad/s and its center of mass has a velocity vo =-7 m/s. The radius of the disk is r = 30 cm, and the coefficient of kinetic friction between the surface and disk is uk = 0.21. Use the conventions that positive velocities are to the right, negative velocities are to the left, positive angular rates are counter-clockwise, and negative rates are clockwise in all cases.

A 9-kg disk has an initial angular rate of wo = +17 rad/s and its center of mass has a velocity vo =-7 m/s. The radius of the disk is r = 30 cm, and the coefficient of kinetic friction between the surface and disk is uk = 0.21. Use the conventions that positive velocities are to the right, negative velocities are to the left, positive angular rates are counter-clockwise, and negative rates are clockwise in all cases.

Elements Of Electromagnetics

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ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Problem 4
A 9-kg disk has an initial angular rate of wo=+17 rad/s and its
center of mass has a velocity vo =–7 m/s. The radius of the disk is
r = 30 cm, and the coefficient of kinetic friction between the
surface and disk is µk = 0.21.
r 21 cm
Use the conventions that positive velocities are to the right,
negative velocities are to the left, positive angular rates are
counter-clockwise, and negative rates are clockwise in all cases.
a. What is an expression, in terms of r, o and v, for
the kinematic condition of rolling without slipping?
b. Draw a clear and complete free body diagram of just the disk in the space provided below.
c. What is the mass moment of inertia of the disk about its center of mass?
d. What is the angular acceleration of the disk?
e. What is the linear acceleration of the disk?
f. For how much time does the disk slide before it begins to roll without slip?
g. What is the velocity of the disk at the instant it begins to roll without slip?
h. For how much distance does the disk slide before it begins to roll without slip?
Side view FBD

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