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$\bullet$ A grindstone in the shape of a solid disk with diameter 0.520 $\mathrm{m}$ and a mass of 50.0 $\mathrm{kg}$ is rotating at 850 $\mathrm{rev} / \mathrm{min.}$ You press an ax against the rim with a normal force of 160 $\mathrm{N}$ (see Figure 10.46 ), and the grindstone comes to rest in 7.50 s. Find the coefficient of kinetic friction between the ax and the grind-stone. There is negligible friction in the bearings.

$\mu_{k}=0.482$

Physics 101 Mechanics

Chapter 10

Dynamics of Rotational Motion

Newton's Laws of Motion

Rotation of Rigid Bodies

Equilibrium and Elasticity

Rutgers, The State University of New Jersey

University of Washington

Hope College

University of Winnipeg

Lectures

02:34

In physics, a rigid body is an object that is not deformed by the stress of external forces. The term "rigid body" is used in the context of classical mechanics, where it refers to a body that has no degrees of freedom and is completely described by its position and the forces applied to it. A rigid body is a special case of a solid body, and is one type of spatial body. The term "rigid body" is also used in the context of continuum mechanics, where it refers to a solid body that is deformed by external forces, but does not change in volume. In continuum mechanics, a rigid body is a continuous body that has no internal degrees of freedom. The term "rigid body" is also used in the context of quantum mechanics, where it refers to a body that cannot be squeezed into a smaller volume without changing its shape.

02:21

In physics, rotational dynamics is the study of the kinematics and kinetics of rotational motion, the motion of rigid bodies, and the about axes of the body. It can be divided into the study of torque and the study of angular velocity.

06:46

A grindstone in the shape …

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A 50.0-kg grindstone is a …

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A $50.0 \mathrm{~kg}$ grin…

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You have a grindstone (a d…

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A wheel in the form of a u…

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A grinding wheel, with a m…

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A disk with a mass of $14.…

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A grinding wheel of radius…

Hello. In problem number nine, we're looking at a grindstone in this shape of a solid cylinder, and it has a diameter of 0.52 meters, which would give us a radius of 0.26 liters. It's mass is 50 kilograms. It's rotating, so it has an initial angular velocity of 850 revolutions per minute. No, that needs to be put into radiance per second version wise, we would want to convert our minutes two seconds. And you know what makes two pi radian revolutions For every revolution you do that conversion you absolute DX 89 90 miles per second way are spending this grindstone and we have used an ax and press it against the rim with a force, uh, 160 Newtons. Friction between that ax and the grindstone actually slowly causes the final velocity to become zero way. We're told that happens in a time period of 7.5 seconds. We are asked to find the co vision of kinetic friction between the acts in the grindstone. You're looking at it. We know we can use these little bit here in this bit of information. No. One of our older kid O Matics Formulas to find are angular acceleration we come to arrest and we started 89 radiance per second and that happens in a time period of 7.5 seconds. We can find our angular acceleration cleaning up a little bit. There are angular acceleration is and negative 11.87 millions per second squared. Okay them Do you find our coefficient of kinetic friction? We go back to the idea that the torque caused by this force is slowing it down. So our net torque is only due to this force or net torque a beak bound. We know it's slowing it down, so we know it's a negative toward and it's found by the friction force times the liberal No friction can be found by you were thin times the lever arm. Now we know the moment of inertia. Formula for a cylinder is 1/2 and r squared. So we know we have just about everything here to Sabian. She'll be able to find our mu or normal horse. Here would be the force applied right here by the ax. So substituting in 1 60 here are level R is our radius of 600.26 our mass of our flywheels 50 and are angular acceleration again from our kin. O Matics isn't Ignat 11.87 solving form you. We find that our coefficient of kinetic friction is point for 82 Thank you for learning with me today.

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