A ball (mass m = 250 g) on the end of an ideal string is moving
in circular motion as a conical pendulum as in the �gure. The
length L of the string is 1.67 m and the angle with
the vertical is 37 degrees
A) What is the magnitude of the angular momentum (kg m2/s) of the ball about the
support point?
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What I have so far.
L = r X P
P = m * v
V = (r*g*tan)^.5
What I am having problems on is finding r, since its at the support point, it will not be the radius of the circle.
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r=1.67*sin37
r would equal that if we were looking at the momentum of the ball about the circle and not at the support point
Use the length of the string for "r".
except for in your equation for the velocity; use the radius of the circle there
To find the magnitude of the angular momentum of the ball about the support point, you need to determine the radius of the circular motion. Since the ball is moving in a conical pendulum, the radius will not be the length of the string.
The useful information provided is the length of the string (L = 1.67 m) and the angle the string makes with the vertical (θ = 37 degrees). With this information, we can determine the radius of the circular motion by using trigonometry.
Let's break down the problem step by step:
1. Draw a diagram of the conical pendulum to visualize the situation. The ball is at the end of the string, and the string is attached to a fixed point at the support.
2. Identify the right triangle formed by the string, the radius, and the vertical direction. The length of the string (L) is the hypotenuse, the radius (r) is the adjacent side, and the angle (θ) is the angle opposite to the radius.
3. Apply trigonometry to find the radius. Since we have the length of the string (L) and the angle (θ), we can use the cosine function:
cos(θ) = Adjacent / Hypotenuse
cos(37 degrees) = r / 1.67 m
Rearrange the equation to solve for r:
r = L * cos(θ)
r = 1.67 m * cos(37 degrees)
Use a calculator to find the numerical value of r.
Now that you have the radius (r), you can proceed to calculate the magnitude of the angular momentum (L) of the ball about the support point using the formula:
L = I * ω
where I is the moment of inertia and ω is the angular velocity.
Since the ball is moving in circular motion, the moment of inertia (I) can be defined as:
I = m * r^2
where m is the mass of the ball.
Finally, the angular velocity (ω) can be calculated using:
ω = v / r
where v is the velocity of the ball.
Once you have calculated the moment of inertia (I) and the angular velocity (ω), you can substitute them into the formula for angular momentum (L).