The angular acceleration of a body, moving along the circumference of a circle, is:
The angular acceleration of a body, moving along the circumference of a circle, is:
along the axis of rotation
along the radius, away from center
along the radius towards the centre
along the tangent to its position
The Correct Option is D
Solution and Explanation
The correct option is (D): along the tangent to its position
Angular acceleration is due to Torque. Suppose there is a plane of a circle, and the body is moving along with the circumference of a circle.
Torque, τ = I x α
I = moment of inertia
and the angular direction is towards the direction of the Torque.
and, the direction of the Torque is, τ = r × F
Where r is the radius and F is the perpendicular tangent.
and the direction of torque is perpendicular to r and perpendicular to F. r and F lie perpendicular to the circle. If the two vectors lie in a circle of a plane, then the cross product of two vectors lies on the perpendicular. And, if the torque lies on the perpendicular of the plane, then the angular acceleration will also lie on the perpendicular of the plane. Hence the correct answer is option D, long the tangent to its position.
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Concepts Used:
Uniform Circular Motion
A circular motion is defined as the movement of a body that follows a circular route. The motion of a body going at a constant speed along a circular path is known as uniform circular motion. The velocity varies while the speed of the body in uniform circular motion remains constant.
Uniform Circular Motion Examples:
- The motion of electrons around its nucleus.
- The motion of blades of the windmills.
Uniform Circular Motion Formula:
When the radius of the circular path is R, and the magnitude of the velocity of the object is V. Then, the radial acceleration of the object is:
arad = v2/R
Similarly, this radial acceleration is always perpendicular to the velocity direction. Its SI unit is m2s−2.
The radial acceleration can be mathematically written using the period of the motion i.e. T. This period T is the volume of time taken to complete a revolution. Its unit is measurable in seconds.
When angular velocity changes in a unit of time, it is a radial acceleration.
Angular acceleration indicates the time rate of change of angular velocity and is usually denoted by α and is expressed in radians per second. Moreover, the angular acceleration is constant and does not depend on the time variable as it varies linearly with time. Angular Acceleration is also called Rotational Acceleration.
Angular acceleration is a vector quantity, meaning it has magnitude and direction. The direction of angular acceleration is perpendicular to the plane of rotation.
Formula Of Angular Acceleration
The formula of angular acceleration can be given in three different ways.
α = dωdt
Where,
ω → Angular speed
t → Time
α = d2θdt2
Where,
θ → Angle of rotation
t → Time
Average angular acceleration can be calculated by the formula below. This formula comes in handy when angular acceleration is not constant and changes with time.
αavg = ω2 - ω1t2 - t1
Where,
ω1 → Initial angular speed
ω2 → Final angular speed
t1 → Starting time
t2 → Ending time
Also Read: Angular Motion