A cord is wrapped around the rim of a solid uniform wheel 0.280m in radius and of mass 8.80kg. A steady horizontal pull of 32N to the right is exerted on the cord, pulling it off tangentially from the wheel. The wheel is mounted on frictionless bearings on a horizontal axle through its center. What is the wheels angular acceleration? What force does the axle apply to the wheel? What torque does the axle apply to the wheel?

Respuesta :

Answer:[tex]25.97 rad/s^2[/tex]

Explanation:

Given

radius of wheel [tex]r=0.28 m[/tex]

mass of wheel [tex]m=8.80 kg[/tex]

Force [tex]F=32 N[/tex]

Moment of Inertia of solid wheel [tex]I=\frac{mr^2}{2}[/tex]

[tex]I=\frac{8.8\times 0.28^2}{2}[/tex]

[tex]I=0.344 kg-m^2[/tex]

Torque is given by

[tex]\tau =F\times r=I\times \alpha [/tex]

[tex]32\times 0.28=0.344\times \alpha [/tex]

[tex]\alpha =25.97 rad/s^2[/tex]

Force on the axle is 32 N since there is no linear acceleration of the system

using Third law F=32 N

Torque of the axle applied to the wheel is zero because force of axle imparted at the center of axle