AF A yoyo is constructed by attaching three uniform, solid disks along their central axes as shown. The two outer disks are identical, each with mass M= 51 g, radius R= 3.9 cm, and moment of inertia 1/2MR². The central, smaller disk has mass M/2 and radius R/2. A light, flexible string of negligible mass is wrapped counterclockwise around the central disk of the yoyo. The yoyo is then placed on a horizontal tabletop and the string is gently pulled with a constant force F = 0.25 N. The tension in the string is not sufficient to cause the yoyo to leave the tabletop. In this problem consider the two cases show. In Case I the string is pulled straight up, perpendicular to the tabletop. In Case 2 the string is pulled horizontally, parallel to the tabletop. In both cases the yoyo rolls without slipping. Case 1: Case 2: Part (a) What is the moment of inertia ICM about the central axis (i.e. the axis perpendicular to the circular face) of the yoyo, in kg m2. ICM-8.242 10-5) ICM - 8.242E-5 V Correct! Part (b) In both cases shown, what is the magnitude of the torque z exerted by the string about the contact point of the yo-yo with the table, in N m? r-0,004881 =4.88IE-3 V Correct! Part (c) What is the moment of inertia of the yo-yo about the contact point with the table, in kg m2? 1= 2.76 * 10( - 4) |= 2.76E-4 V Correct! Part (d) What is the magnitude of the linear acceleration of the center of mass of the yoyo the moment the string becomes taut, in m/s. асм-
AF A yoyo is constructed by attaching three uniform, solid disks along their central axes as shown. The two outer disks are identical, each with mass M= 51 g, radius R= 3.9 cm, and moment of inertia 1/2MR². The central, smaller disk has mass M/2 and radius R/2. A light, flexible string of negligible mass is wrapped counterclockwise around the central disk of the yoyo. The yoyo is then placed on a horizontal tabletop and the string is gently pulled with a constant force F = 0.25 N. The tension in the string is not sufficient to cause the yoyo to leave the tabletop. In this problem consider the two cases show. In Case I the string is pulled straight up, perpendicular to the tabletop. In Case 2 the string is pulled horizontally, parallel to the tabletop. In both cases the yoyo rolls without slipping. Case 1: Case 2: Part (a) What is the moment of inertia ICM about the central axis (i.e. the axis perpendicular to the circular face) of the yoyo, in kg m2. ICM-8.242 10-5) ICM - 8.242E-5 V Correct! Part (b) In both cases shown, what is the magnitude of the torque z exerted by the string about the contact point of the yo-yo with the table, in N m? r-0,004881 =4.88IE-3 V Correct! Part (c) What is the moment of inertia of the yo-yo about the contact point with the table, in kg m2? 1= 2.76 * 10( - 4) |= 2.76E-4 V Correct! Part (d) What is the magnitude of the linear acceleration of the center of mass of the yoyo the moment the string becomes taut, in m/s. асм-
Principles of Physics: A Calculus-Based Text
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Chapter10: Rotational Motion
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Problem 56P: A student sits on a freely rotating stool holding two dumbbells, each of mass 3.00 kg (Fig. P10.56)....
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Question
Transcribed Image Text:A yoyo is constructed by attaching three uniform, solid disks along their
central axes as shown. The two outer disks are identical, each with mass M= 51 g, radius R= 3.9
AF
cm, and moment of inertia 1/2MR². The central, smaller disk has mass M/2 and radius R/2. A light,
flexible string of negligible mass is wrapped counterclockwise around the central disk of the
The yoyo is then placed on a horizontal tabletop and the string is gently pulled with a constant
force F = 0.25 N. The tension in the string is not sufficient to cause the yoyo to leave the tabletop.
In this problem consider the two cases show. In Case 1 the string is pulled straight up,
perpendicular to the tabletop. In Case 2 the string is pulled horizontally, parallel to the tabletop. In
both cases the yoyo rolls without slipping.
yoyo.
Case 1:
I
F
Case 2:
Part (a) What is the moment of inertia ICM about the central axis (i.e. the axis perpendicular to the circular face) of the yoyo, in kg•m².
ICM= 8.242 * 10(- 5 )
ICM= 8.242E-5 / Correct!
Part (b) In both cases shown, what is the magnitude of the torque t exerted by the string about the contact point of the yo-yo with the table, in
N m?
7 = 0.004881
7= 4.881E-3
Correct!
Part (c) What is the moment of inertia of the yo-yo about the contact point with the table, in kg m²?
I= 2.76 * 10( - 4)
I= 2.76E-4
Correct!
Part (d) What is the magnitude of the linear acceleration of the center of mass of the yoyo the moment the string becomes taut, in m/s².
асм
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