I want full concept of rotational dynamic.
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Answer:
We have defined the angular displacement, angular speed and angular velocity, angular acceleration, and kinetic energy of an object rotating about an axis. These definitions apply to objects spinning about an internal axis, such as a wheel spinning on its axle, or to objects revolving around a point external to the objects, such as the earth revolving around the sun.
A spinning or revolving object has angular velocity ω. Whenever the magnitude or direction of this angular velocity changes, the object has angular acceleration α.
What causes angular acceleration?
imageAssume you want to change a rotating wheel's angular speed. To increase the angular speed you probably will apply a force to the rim, tangential to the rim, and in the direction of the instantaneous velocity of the section of the rim to which you apply the force.
If you want to decrease the angular speed, you will reverse the direction of the force.
imageAssume you want to enter a building with a rotating door. The door has four panels, and you push on one of them, perpendicular to the surface of the panel.
The rate, at which the angular velocity of the door changes, i.e. the angular acceleration α, is greater the farther away from the axis of rotation you apply the force.
Angular acceleration about a point is the result of a torque about this point. A torque is the product of a lever arm and a force that is applied perpendicular to the lever arm. The lever arm or moment arm is the perpendicular distance from the center of rotation, i.e. from the pivot point, to the point where the force is applied.
A torque is always defined with respect to a pivot point.
A larger torque produces a larger angular acceleration. You can get a larger torque by applying a larger force, or by using a longer lever arm. We write
torque = lever arm × force,
imageTorque is a vector. It is the vector product or cross product of r and F.
If a force F acts on an object, then the torque produced by this force about a pivot point is τ = r × F, where r is a displacement vector pointing from the axis of rotation to the point where the force is applied.
The SI units of torque are Nm.
Torque has magnitude and direction.
Its direction is given by the right-hand rule.
Let the fingers of your right hand point from the axis of rotation to the point where the force is applied.
Curl them into the direction of F.
Your thumb points in the direction of the torque vector.
The magnitude of the torque τ is τ = rFsinθ, where θ is the smallest angle between the directions of the vectors r and F.
We can also write τ = rperpF = rFperp, where rperp is the component of the lever arm perpendicular to F, or where Fperp is the component of F perpendicular to the lever arm.
If two or more forces act on an object, then the net torque is the vector sum of the torques produced by the separate forces. (For rotations about a single axis, two torques can point in the same direction or in opposite directions and therefore can add or subtract.)
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Answer
Rotational dynamics. We have defined the angular displacement, angular speed and angular velocity, angular acceleration, and kinetic energy of an object rotating about an axis. ... Whenever the magnitude or direction of this angular velocity changes, the object has angular acceleration α.