Calculating angular acceleration of a wire

In summary, a rigid horizontal wire with mass M and constant current I, pivoted at P, rotates at a constant angular speed in a uniform vertical magnetic field B. If the current is switched off, the wire's angular acceleration can be calculated using the equation (3BI)/(2M). The moment of inertia for a rod about one end is (MR^2)/3. The torque can be calculated using the equation BIR^2sin(angle), but the angle in this case is not specified. If the angle is 45 degrees, the correct answer would be (3BI)/(M*sqrt(2)). However, it is not specified if the wire is rotating in a horizontal plane in a vertical field with all angles at right
  • #1

Homework Statement


A rigid uniform horizontal wire PQ of mass M, pivoted at P, carries a constant current I. It rotates with a constant angular speed in a uniform vertical magnetic field B. If the current were switched off, the angular acceleration of the wire in terms of B, M and I would be
[It is not shown here, but in the diagram, PQ is the radius. P is the centre]

ans= ( 3BI ) / ( 2M )

Homework Equations


(angular acceleration) = (torque) / (Moment of Inertia)
(Moment of Inertia) = (MR^2) / 3 for a rod about one end
(Torque) = Force * Radius sin(angle between them)

The Attempt at a Solution



M of I = ( MR^2) / 3
Torque = Force * R
= BIR^2sin( angle between them)

My problem is here. Is the angle 45 degrees? If it is, shouldn't the answer be (3BI)/M*root2?

Also, if current is switched off, the only force acting is B. Even then the rod will be rotating for some time. But current will not be induced as the field is uniform. I am terribly confused.
 
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  • #2
I believe it is rotating in a horizontal plane in a vertical field. All angles are right angles, no?
 

1. What is angular acceleration?

Angular acceleration is a measure of how quickly the angular velocity of an object changes over time. It is expressed in units of radians per second squared (rad/s^2).

2. How do you calculate angular acceleration?

Angular acceleration can be calculated by taking the change in angular velocity over a given period of time. The formula for angular acceleration is: α = (ω2 - ω1) / (t2 - t1), where α is the angular acceleration, ω1 and ω2 are the initial and final angular velocities, and t1 and t2 are the initial and final times.

3. What is the difference between linear and angular acceleration?

Linear acceleration is the rate of change of an object's linear velocity, while angular acceleration is the rate of change of an object's angular velocity. Linear acceleration is measured in units of meters per second squared (m/s^2), while angular acceleration is measured in units of radians per second squared (rad/s^2).

4. How does the mass of the wire affect its angular acceleration?

The mass of the wire does not directly affect its angular acceleration. However, the distribution of the mass along the wire, as well as any external forces acting on the wire, can affect its moment of inertia and therefore its angular acceleration.

5. Can angular acceleration be negative?

Yes, angular acceleration can be negative. This indicates that the object is decreasing in angular velocity over time, or decelerating. A positive angular acceleration indicates an increasing angular velocity over time, or acceleration.

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