Angular Acceleration of a Wheel A wheel of radius R = 20.5 cm, mass M= 2.93 kg,

Question

Angular Acceleration of a Wheel A wheel of radius R = 20.5 cm, mass M= 2.93 kg, and moment of inertia I is mounted on a frictionless, horizontal axle as in the figure. A light cord wrapped around the wheel supports an object of mass m = 0.602 kg. Calculate the angular acceleration of the wheel, the linear acceleration of the object, and the tension in the cord SOLVE IT Conceptualize: Imagine that the object is a bucket in an old-fashioned wishing well. It is tied to a cord that passes around a cylinder equipped with a crank for raising the bucket. After the bucket has been raised, the system is released and the bucket accelerates downward while the cord unwinds off the cylinder. Categorize: The object is modeled as a particle under a net force The wheel is modeled as a rigid object under a net torque Analyze: The magnitude of the torque acting on the wheel about its axis of rotation is -TR, where T is the force exerted by the cord on the rim of the wheel. (The gravitational force exerted by the Earth on the wheel and the normal force exerted by the axle on the wheel both pass through the axis of rotation and therefore produce no torque.) An object hangs from a cord wrapped around a wheel Use the following equation: …2 Solve for and substitute the net torque: (1)

Explanation / Answer

4) I for disc = 0.5 MR^2

T =mg/{1 +mr^2/I} = 0.602×9.8/{1+ 2×0.602/2.93}

= 4.18 N

a = (T-mg)/m = -9.8 + 4.18/0.602 = -2.86 m/s

at maximum height h, the velocity will be zero because acceleration is negative

V^2 = u^2 - 2ah

0= 4.67^2 - 2×2.86×h

h =3.81 m Answer

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