losses and assume that the mass of the ball is distributed uniformly. If the lin
ID: 2102000 • Letter: L
Question
losses and assume that the mass of the ball is distributed uniformly. If the linear speed of the ball is
11.5 ft/s at the bottom of the rise, find the linear speed of the ball at the top. Hint: the ball is rotating
without slipping the entire time.
10. A woman stands in the middle of a small rowboat. The rowboat is floating freely and experiences
no friction against the water. The woman is initially facing east. If she turns around 180o so that
she faces west, through what angle will the rowboat turn? Assume that the woman performs her
turning movement at constant angular velocity and that her moment of inertia remains constant
during this movement. The moment of inertia of the rowboat about the vertical axis is 20 kg m2
and that of the woman is 0.80 kg m2 .
11. Galileo measure the acceleration of gravity by rolling a sphere down an inclined plane. Suppose
that, starting from rest, a sphere takes 1.6 s to roll a distance of 3.00 m down a 20o inclined
plane. What value of g can you deduce from this?
12. A wheel, with radius .5 m and moment of inertia 50 kg m2 about its center, rotates about a
frictionless axle with angular velocity 10 radians per second. A brake is applied which supplies a
constant force to a point on a the perimeter of the wheel of 10 N, tangent to the wheel and opposing
the motion. How many revolutions will the wheel make before coming to rest?
Explanation / Answer
angular momentum is conserved;
so, I1*w1*t=I2*w2*t
=> w1*t= 0.8*pi/20
=> w1*t= 0.125 rad
=> w1*t=7.2 degree
B) S= u*t +0.5*asin20*t^2
=> a= 2*S/t^2*sin20
=> a= 2*3/1.6^2*sin20
=> a= 6.85 m/s^2
C) mass=I/r^2
=200 kg
acceleration= 10/200 m/s^2
=0.05 m/s^2
alpha=a/r
=0.05/0.5
0.1 rad/s^2
angular distance=w^2/(2*alpha)
=100/(2*0.1)
=500 rad
No. of revolution=500/(2*pi)
=79.57 times
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