Physics help A stationary bicycle wheel of radius 0.8 m is mounted in the vertic
ID: 1467277 • Letter: P
Question
Physics help A stationary bicycle wheel of radius 0.8 m is mounted in the vertical plane (see figure below). The axle is held up by supports that are not shown, and the wheel is free to rotate on the nearly fricbonless axle. The wheel has mass 4.7 kg, all concentrated in the rim (the spokes have negligible mass). A lump of clay with mass 0.5 kg falls and sticks to the outer edge of the wheel at the location shown. Just before the impact the clay has speed 8 m/s, and the wheel is rotating clockwise with angular speed 0.29 rad/s. (Assume +x is to the right, +y is upward, and +7 is out of the page. Assume the line connecting the center to the point of impact is at an angle of 45 degree from the horizontal.) Just before the impact, what is the angular momentum (magnitude and direction) of the combined system of wheel plus day about the center C? Just after the impact, what is the angular momentum (magnitude and direction) of the combined system of wheel plus clay about the center C? Just after the impact, what is the angular velocity (magnitude and direction) of the wheel? Qualitatively, what happens to the linear momentum of the combined system? Why? Qualitatively, what happens to the linear momentum of the combined system? Why?Explanation / Answer
radius of the wheel, r=0.8 m
mass of the wheel is M=4.7 kg
mass of the clay m=0.5 kg
speed of the clay v=8 m/sec
angular speed w=0.29 rad/sec
theta=45 degrees,
a)
before the impact,
angular momentum,L=m*v*r*sin(theta)
L=0.5*8*0.8*sin(45)
L=2.26 kg.m^2/sec ( along z axis)
b)
after impact,
angular momentum is same as in part(a)
L=2.26 kg.m^2/sec ( along z axis)
c)
here,
L=I*wf
wf=L/I
=2.26/(M*r^2+m*r^2)
=2.26/((4.7+0.5)*0.8^2)
=0.68 rad/sec ( along z axis)
d)
correct option is,
downward linear momentum decreases because the axle exerts an upwards force