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$\bullet$ A 750 gram grinding wheel 25.0 $\mathrm{cm}$ in diameter is in the shape of a uniform solid disk. (We can ignore the small hole at the center.) When it is in use, it turns at a constant 220 $\mathrm{rpm}$ about an axle perpendicular to its face through its center. When the power switch is turned off, you observe that the wheel stops in 45.0 s with constant angular acceleration due tofriction at the axle. What torque does friction exert while this wheel is slowing down?

$3.00 \times 10^{-3} \mathrm{N.m}$

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

Simon Fraser University

Hope College

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.

04:21

A 750 g grinding wheel $25…

02:18

A grinding wheel, with a m…

04:28

A grindstone in the shape …

06:46

01:02

A grinding wheel of radius…

05:07

$\bullet$ A grindstone in …

02:26

A uniform cylindrical grin…

07:27

A flat cylindrical grindin…

06:44

04:41

A wheel with radius $0.060…

03:00

A wheel in the form of a u…

01:48

You are holding the axle o…

So here we have a uniform solid disc and the moment of inertia for this is going to be I equals half em are squared. We're going to say that we rather we know that the mass is equaling 0.750 kilograms or 750 grams. Our equals point 12 5,000,000 rather meters and omega initial equals 220 revolutions per minute. And we're going to convert this to radiance per second 23.4 radiance per second. At this point, we know that it is coming to arrest. So the final angular velocity is radio is zero radiance per second and we can find the angular acceleration by taking Omega final minus omega initial divided by Delta T. We know that Omega Final is zero. So this will simply be equal to negative 23.4 divided by 45 seconds. And this is equaling negative 450.512 radiance per second squared. We know that in order to find the sum of the torque, this is going to be equal to the moment of inertia, times the angular acceleration. This is going to be equal to half m r squared times, Alfa. And at this point, we can solve and say 1/2 times 0.75 times 0.125 squared time's Alfa of negative 0.512 and we're getting that The net torque is going to be equal to negative 0.3 new leaders. And again, this because it's negative, were going to say that this direction is direction is going to be opposite of direction of motion. And that is the end of the solution. Thank you for watching.

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