Problem 6: 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 = 62 g, radius R = 2.1 cm, and moment of inertia 1/2MR. 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 = 0.325 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 IN I tabletop In both cases the vovo rolls without slipping

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8.6 please answer part d, other parts are answered

Problem 6: 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 = 62 g,
F
radius R = 2.1 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 = 0.325 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.
RĪ
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.
Numeric : A numeric value is expected and not an expression.
ICM =
2.9 E -5
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?
Numeric : A numeric value is expected and not an expression.
T =
00 341
Part (c) What is the moment of inertia of the yo-yo about the contact point with the table, in kg•m2?
Numeric : A numeric value is expected and not an expression.
I =
9.74E -5
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?.
Numeric : A numeric value is expected and not an expression.
асм —
Transcribed Image Text:Problem 6: 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 = 62 g, F radius R = 2.1 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 = 0.325 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. RĪ 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. Numeric : A numeric value is expected and not an expression. ICM = 2.9 E -5 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? Numeric : A numeric value is expected and not an expression. T = 00 341 Part (c) What is the moment of inertia of the yo-yo about the contact point with the table, in kg•m2? Numeric : A numeric value is expected and not an expression. I = 9.74E -5 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?. Numeric : A numeric value is expected and not an expression. асм —
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