A rectangular plate of mass 20 kg is suspended from points A and B as shown. If the pin B is su

A rectangular plate of mass 20 kg is suspended from points...

Key Concepts

Center of Mass

The center of mass is the point at which an object's mass is considered to be concentrated when analyzing motion. In rotational dynamics, its location determines the lever arm for gravitational or other forces, influencing the resulting torque and hence the angular acceleration.

Moment of Inertia

The moment of inertia is a property of a body that quantifies its resistance to angular acceleration about a specific axis. It depends on both the total mass of the object and how that mass is distributed relative to the axis of rotation, playing a role similar to mass in linear motion.

Torque

Torque is the measure of the rotational effectiveness of a force acting on a body. It is calculated as the product of the force and the perpendicular distance from the pivot or axis of rotation to the line of action of the force. Torque determines how strongly a force tends to produce rotational acceleration.

Newton's Second Law for Rotation

Newton's second law for rotation states that the net torque acting on an object is equal to the product of its moment of inertia and its angular acceleration (? = I?). This principle is the rotational analogue of the linear form of Newton's second law, connecting force (torque), mass distribution, and acceleration.

Transcript

00:01 In this question we have given a rectangular plane of mass 20 kilograms and is suspended from point a and b now it is told that the point b is suddenly removed we have to find the angular acceleration of this plate now let when plate starts to rotate about point a then we can say that torque is given by that is i into alpha and we can say that torque is given by that is i into alpha and we can say that this torque is equal to this weight that is mg into distance from point a that is l by 2 and this is equals to i alpha now because this is our rectangular plate and this is suspended at this two point this is point a and this now this point is cut so we can say that there is the weight is acting vertically downward that is mg and this distance is known to us that is l by 2 this is is point a so we can say that this torque due to this torque this will rotate in this direction and this angular acceleration is alpha now we have given that l is equal to 0 .2 and we have given the value of b that is 0 .15 meter now we know that let this is the this distance is d so we can say that this is equals to this distance is b by 2 because this distance is b and this is the center of the place so from here we can say that d square is equal to this is l square by 4 plus b square by 4 so this will come out to be 0 .0625 upon 4 this is the value of d square now we can say that moment of inertia about the axis of rotation is given by that is moment of inertia about center of mass plus m into d square because this will start about rotating about this point so we have to find this distance so from here we can say this is equal to m upon 12 l square plus d square now put all the data in this equation so this is m l square plus b square plus this is m into d square so we can say this will come so to be 20 upon 12 this is 0 .2 square plus 0 .15 square plus this is 20 into now put the value of d square so this is 0 .0 .0 .0 0625 upon 4 after solving this we get now this is the value of moment of inertia i now we have from this equation we can say that let this is our equation first so we can say from equation first that is i alpha is equal to this is m g into l by 2 from here we can say that alpha is given by that is m g l upon 2 i now put all the data in this equation so this is 20 into 10 into l is 0 .2 upon 2 now put the value of i here so this is 20 by 12 into 0 .2 square plus 0 .5 square sorry this is 0 .15 square plus 20 into this is 0 .6 25 upon 4 so after solving this whole calculation we find this is 48 radiance per second so this is the angular radiation of the plate, sorry angular acceleration and this is our answer...

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