The circular disk of 270-mm radius has a mass of 36 kg with centroidal radius of gyration k⎯⎯k¯ = 235 mm and has a concentric circular groove of 105-mm radius cut into it. A steady force T is applied at an angle θ to a cord wrapped around the groove as shown. If T = 59 N, θ = 29°, μs = 0.08, and μk = 0.07, determine the angular acceleration α of the disk, the acceleration a of its mass center G, and the friction force F which the surface exerts on the disk. The angular acceleration α is positive if counterclockwise, negative if clockwise; the acceleration a

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The circular disk of 270-mm radius has a mass of 36 kg with centroidal radius of gyration k⎯⎯k¯ = 235 mm and has a concentric circular groove of 105-mm radius cut into it. A steady force T is applied at an angle θ to a cord wrapped around the groove as shown. If T = 59 N, θ = 29°, μs = 0.08, and μk = 0.07, determine the angular acceleration α of the disk, the acceleration a of its mass center G, and the friction force F which the surface exerts on the disk. The angular acceleration α is positive if counterclockwise, negative if clockwise; the acceleration a is positive if to the right, negative if to the left; and the friction force F is positive if to the right, negative if to the left..

The circular disk of 270-mm radius has a mass of 36 kg with centroidal radius of gyration k = 235 mm and has a concentric circular
groove of 105-mm radius cut into it. A steady force T is applied at an angle to a cord wrapped around the groove as shown. If T = 59N,
0 = 29°, μs = 0.08, and μk = 0.07, determine the angular acceleration a of the disk, the acceleration a of its mass center G, and the
friction force F which the surface exerts on the disk. The angular acceleration a is positive if counterclockwise, negative if clockwise;
the acceleration a is positive if to the right, negative if to the left; and the friction force F is positive if to the right, negative if to the left.
m= 36 kg
k 235 mm
270 mm
T
G
Ug = 0.08
Uh = 0.07
105
mm.
Transcribed Image Text:The circular disk of 270-mm radius has a mass of 36 kg with centroidal radius of gyration k = 235 mm and has a concentric circular groove of 105-mm radius cut into it. A steady force T is applied at an angle to a cord wrapped around the groove as shown. If T = 59N, 0 = 29°, μs = 0.08, and μk = 0.07, determine the angular acceleration a of the disk, the acceleration a of its mass center G, and the friction force F which the surface exerts on the disk. The angular acceleration a is positive if counterclockwise, negative if clockwise; the acceleration a is positive if to the right, negative if to the left; and the friction force F is positive if to the right, negative if to the left. m= 36 kg k 235 mm 270 mm T G Ug = 0.08 Uh = 0.07 105 mm.
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