What is the Mass of the Uniform Disk Used as a Cam on a Vertical Shaft?

In summary, the mass of the uniform disk, attached to a vertical shaft and used as a cam with a diameter of 38 cm and a moment of inertia of 7.5*10^-3 kg*m/s about the axis of the shaft, is closest to 0.14 kg. This is determined using the parallel axis theorem and the given angular velocity of 70 rpm.
  • #1
Soaring Crane
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A uniform disk is attached at the rim to a vertical shaft and is used as a cam. The disc has a diameter of 38 cm. The moment of inertia of the disk about the axis of the shaft is 7.5*10^-3 kg*m/s. The shaft rotates uniformly about its axis at 70 rpm. The mass of the disc is closest to:

a.0.12 kg
b. 0.092 kg
c. 0.14 kg
d. 0.18
e.0.16 kg

I don’t know why the angular velocity is given. This is what I managed to do:

Using parallel axis theorem,

I_p = I_cm + M*d^2 = 0.5*M*r^2 + M*r^2 = 1.5*M*r^2

M = (I_p)/(1.5*r^2) = (0.0075 kg*m/s)/(1.5*.19 cm^2) = 0.1385 kg

Thanks.
 
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  • #2
Is this the right track?

Thanks again.
 
  • #3
Looks good to me.
 

FAQ: What is the Mass of the Uniform Disk Used as a Cam on a Vertical Shaft?

What is moment of inertia?

Moment of inertia is a measurement of an object's resistance to rotational motion. It is similar to mass in linear motion, but instead measures an object's distribution of mass around a rotational axis.

How is moment of inertia calculated for a disk?

The moment of inertia for a disk can be calculated by using the formula I = 1/2 * MR^2, where M is the mass of the disk and R is the radius of the disk.

How does the moment of inertia change for a disk with varying mass and radius?

As the mass or radius of a disk changes, the moment of inertia also changes. A disk with a larger mass or radius will have a larger moment of inertia, meaning it will be more resistant to rotational motion.

What is the relationship between moment of inertia and angular velocity?

The moment of inertia and angular velocity are inversely related. This means that as the moment of inertia of an object increases, the angular velocity decreases, and vice versa.

How does moment of inertia affect the stability of a disk?

The moment of inertia plays a crucial role in the stability of a disk. The larger the moment of inertia, the more stable the disk will be, as it will be less likely to rotate or topple over when subjected to external forces.

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