A safety table saw uses a braking system to stop the saw blade from rotating if it senses that the blade is touching the user’s finger. To avoid injuring the finger, the blade must be stopped within the time that it would take the blade to rotate about 1/20 of a turn at full speed. Assume that the saw blade is essentially a flat disk with mass M and radius R, and rotates once in time T at full speed. (a)What is the magnitude I F I of the constant force that the brake must exert on the rim when tripped? (b) If the saw blade has a radius of 13 cm, a mass of 600 g, and rotates at 3000 rpm, what is I F I? (The braking system used in safety saws exerts this enormous force by jamming a soft aluminum block into the blade’s teeth. The force is exerted as a result of the teeth burying themselves in the block.)
Angular Momentum
The momentum of an object is given by multiplying its mass and velocity. Momentum is a property of any object that moves with mass. The only difference between angular momentum and linear momentum is that angular momentum deals with moving or spinning objects. A moving particle's linear momentum can be thought of as a measure of its linear motion. The force is proportional to the rate of change of linear momentum. Angular momentum is always directly proportional to mass. In rotational motion, the concept of angular momentum is often used. Since it is a conserved quantity—the total angular momentum of a closed system remains constant—it is a significant quantity in physics. To understand the concept of angular momentum first we need to understand a rigid body and its movement, a position vector that is used to specify the position of particles in space. A rigid body possesses motion it may be linear or rotational. Rotational motion plays important role in angular momentum.
Moment of a Force
The idea of moments is an important concept in physics. It arises from the fact that distance often plays an important part in the interaction of, or in determining the impact of forces on bodies. Moments are often described by their order [first, second, or higher order] based on the power to which the distance has to be raised to understand the phenomenon. Of particular note are the second-order moment of mass (Moment of Inertia) and moments of force.
A safety table saw uses a braking system to stop the saw blade from rotating if it senses that the blade is touching the user’s finger. To avoid injuring the finger, the blade must be stopped within the time that it would take the blade to rotate about 1/20 of a turn at full speed. Assume that the saw blade is essentially a flat disk with mass M and radius R, and rotates once in time T at full speed.
(a)What is the magnitude I F I of the constant force that the brake must exert on the rim when tripped?
(b) If the saw blade has a radius of 13 cm, a mass of 600 g, and rotates at 3000 rpm, what is I F I? (The braking system used in safety saws exerts this enormous force by jamming a soft aluminum block into the blade’s teeth. The force is exerted as a result of the teeth burying themselves in the block.)
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