how many revolutions are completed by a top spinning with a constant angular velocity of 3pi radians during a 20 sec time interv
1 answer:
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Answer:
Xcm = 1.95 cm and Ycm = 1.76 cm
Explanation:
The very useful concept of mass center is
R cm = 1/M ∑
Where ri, mi are the mass positions of the bodies from some reference point by selecting and M is the total mass of the body.
Let's look for the total mass
M = m₁ + m₂ + m₃
M = 140 + 45 + 85
M = 270 g
Let's look for the position of each point
Point 1. top vertex, if the triangle has as side d
R₁ = d / 2 i ^ + d j ^
R₁ = (1.7 cm i ^ + 3.4 j ^) cm
Point 2. left vertex. What is the origin of the system?
R₂ = 0
Point 3. Right vertex
R₃ = d i ^
R₃ = 3.4 i ^ cm
a) The x component of the massage center
Xcm = 1 / M (m₁ x₁ + m₂ x₂ + m₃ x₃)
Xcm = 1 / M (m₁ d / 2 + 0 + m₃ d)
Xcm = d / M (m₁ / 2 + m₃)
b) Let's write the mass center component x
Xcm = 1/270 (1.7 140 + 0 + 3.4 85)
Xcm = 238/270
Xcm = 1.95 cm
c) let's find the component and center of mass
Ycm = 1 / M (m₁ y₁ + m₂ y₂ + m₃ y₃)
Ycm = 1 / M (m₁ d + 0 + 0)
Ycm = m₁ / M d
d) let's calculate
Y cm = 1/270 (140 3.4 + 0 + 0)
Ycm = 1.76 cm