Solving Center of Mass Prob: Stick Length 0.25m, Mass 0.53kg

In summary, a girl throws a stick with a length of 0.25 m and a mass of 0.53 kg into the air, causing it to make 33 complete revolutions before reaching its highest point. The stick's cross-sectional area and mass are uniform, and the acceleration of gravity is 9.8 m/s^2. To find the time it takes for the center of mass to reach its highest point, one can use the relationship between angular speed and time, as well as the relationship between the speed of the center of mass and the angular speed of the stick. This information was helpful to the original poster.
  • #1
SsUeSbIaEs
17
0
Can someone please help me with this problem, a hint, anything something?

A girl throws a stick with a length of 0:25 m
and a mass of 0.53 kg into the air in such a
way that the center of mass rises vertically.
At the moment it leaves her hand, the stick
is horizontal and the speed of the end of the
stick nearest to her is zero. When the center
of mass of the stick reaches its highest point,
the stick is horizontal, and it has made 33
complete revolutions. Assume that the stick's
cross sectional area and mass is uniform.
The acceleration of gravity is 9.8 m/s^2 (speed of stick end
is zero when it leaves her hand)
How long did it take for the center of mass
to reach its highest point? Answer in units of
s.
 
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  • #2
Originally posted by SsUeSbIaEs
Can someone please help me with this problem, a hint, anything something?
Realize that you can express the angular speed ω of the stick in terms of the time it takes to get to the top, which is what you are trying to find. Also realize that at the moment the stick is released, the speed of the center of mass is related to the angular speed of the stick: V=ωR. Then apply what you (I hope) know about accelerated motion.
 
  • #3
Thanks that helped a lot!
 

What is the formula for calculating the center of mass of an object?

The formula for calculating the center of mass of an object is: xcm = (m1x1 + m2x2 + m3x3 + ... + mnxn) / (m1 + m2 + m3 + ... + mn), where xcm is the center of mass, mi is the mass of each individual component, and xi is the position of each component along the axis being measured.

How do I find the center of mass of a stick with a given length and mass?

To find the center of mass of a stick with a given length and mass, you will need to know the position and mass of each individual component of the stick. Once you have this information, you can use the formula for calculating the center of mass to determine the exact location of the center of mass along the stick's length.

What is the significance of finding the center of mass of an object?

The center of mass is an important concept in physics and engineering as it represents the point at which an object's mass is evenly distributed. This point can help determine how an object will behave under certain forces and is crucial in understanding the stability and balance of an object.

How does changing the length or mass of a stick affect its center of mass?

Changing the length or mass of a stick will directly affect its center of mass. The longer the stick, the further the center of mass will be from one end. Similarly, increasing the mass of the stick will cause the center of mass to shift closer to the heavier end. This relationship is described by the formula for calculating the center of mass.

Can the center of mass be located outside of the object?

No, the center of mass must always be located within the object itself. This is because the center of mass is a point that represents the average position of all the mass in an object. If the center of mass were located outside of the object, it would mean that there is mass located outside of the object, which is not possible.

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