source : utexas.edu

## Worked example 8.5: Hinged rod

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Question: A uniform rod of mass

and length

rotates about a fixed frictionless pivot located at one of its ends. The rod is released from

rest at an angle

beneath the horizontal. What is the angular acceleration

of the rod immediately after it is released?

Answer: The moment of inertia of a rod of mass and length about

an axis, perpendicular to its length, which passes through one of its ends is

(see question 8.3). Hence,

The angular equation of motion of the rod is

where is the rod’s angular acceleration, and is the net torque exerted on the

rod. Now, the only force acting on the rod (whose line of action does not pass through

the pivot) is the rod’s weight, . This force acts at the centre of mass of the rod,

which is situated at the rod’s midpoint. The perpendicular distance between the

line of action of the weight and the pivot point is simply

Thus, the torque acting on the rod is

It follows that the rod’s angular acceleration is written

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Up: Rotational motion

Previous: Worked example 8.4: Weight

Richard Fitzpatrick

2006-02-02

The dimensions of angular acceleration is what – Brainly.in – Angular acceleration = Rate of change of angular velocity. Find the angular acceleration of the rod about the axis immediately after the thread breaks.The angular acceleration is also shown in the figure. Newton's second law for rotation defines that this vector must always be parallel to the sum of the torques, since Do not forget to include the units in the results. The post Rotational motion – Angular acceleration of a rod appeared first on YouPhysics.The angular acceleration α of a rotating body is its rate of change of angular velocity ω. If a small angular velocity where <v> is the average velocity, ω0 is the initial angular velocity and ω is the finial velocity (both in rad s-1 after the body has rotated through angular displacement θ (rad) with…

Rotational motion – Angular acceleration of a rod – What is the angular acceleration of the rod immediately after it is released? The moment of inertia of a rod about the center of mass is 1/12mL2 , where m is the mass of the rod and L is the length of the Angular Acceleration? A uniform 8 kg rod with length 30 m has a frictionless pivot at one end.What is the angular acceleration of the rod immediately after it is released? Take the counterclockwise direction to be positive.The rod is released from rest at an angle of 23degrees beneath the horizontal. The moment ofinertia of a rod about either end is 1/3 mL2 , and the acceleration of gravity is 9.8 m/s2 . Answer in units of rad/s2.

Angular Acceleration – What is the angular acceleration α of the rod immediately after it is released? Take the counterclockwise direction to be positive. Express α in terms of some or all of the variables mr, m1, m2, x, I, and g.What is the angular speed ωf of the system immediately after the collision, in terms of system parameters and I? Question. A rod of mass M and length L can rotate about a hinge at its left end and is initially at rest. A putty ball of mass m, moving with speed V…Angular acceleration (α) can be defined as angular velocity (ω) divided by acceleration time (t). Alternatively, pi (π) multiplied by drive speed (n) Nonetheless it is still very helpful in approximating torque requirements or establishing baseline minimum values for component sizing purposes.