A wheel (radius = 0.30 m is mounted on a frictionless, horizontal axis. A light

Question

A wheel (radius = 0.30 m is mounted on a frictionless, horizontal axis. A light cord wrapped around the wheel supports a 0.50 - kg object. When released from rest the object falls with a downward acceleration of5.0 m/sec^2. Find the tension on the cord. Find the angular acceleration of the wheel. Find the moment of inertia of the wheel. A solid disk (M=10kg and R = 70 cm) is rotating at 300 rpm initially. Then a smaller ring (m=30 kg and r =40 cm) is dropped concentrically onto the disk and they rotate together with a new angular velocity. find the final angular velocity of the system in rpm. find the change in rotational kinetic energy of the system. find the percent of energy loss during this collision between the solid disk and the ring. A hollow spherical ball is let go from the top of a track and goes around a circular loop (R= 60 cm). What must be the minimum height of the track so that the ball will not fall off the track at the topmost point of the loop? When the above condition is met, what is the tangential speed of the ball when it reaches the topmost point?

Explanation / Answer

19 ans

Given that

mass of block m=0.5 kg

radius r=0.3 m

acceleration a=5 m/s^2

basing on the concept of rotational dynamices

now we find the moment of inertia

a=mg/(m+M/2)

m+M/2=0.5*9.8/5

0.5+M/2=0.98

M/2=0.48

M=0.96 kg

mass of the wheel M=0.96 kg

the moment of inertia of the wheel I=0.96*0.3^2=0.0864 kg.m^2

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