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Question
For a particle performing uniform circular motion, choose the correct statement (s) from the following :
For a particle performing uniform circular motion, choose the correct statement (s) from the following :
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Solution
The correct option is D Magnitude of particle velocity (speed) remains constant.
Definition: Uniform circular motion: It can be described as motion of an object in a circle at a constant speed.
Step 1: Find the speed and velocity of the particle.
when an object moves in a circle, it is constantly changing its direction. At all instances, the object is moving tangent to the circle. Since the direction of the velocity vector is the same as the direction of the object's motion, the velocity vector is directed tangent to the circle or perpendicular to the radius vector. As motion is uniform so, speed remains constant.
Step 2: Find the acceleration of the particle.
Hint: Tangential acceleration measure how the tangential velocity of a point in circular motion changes with time.
As in uniform circular motion tangential speed of the particle remains constant. Therefore, tangential acceleration of the particle will be zero.
Particle will have only centripetal acceleration (as it moves in a circle), and direction of centripetal acceleration is always towards the centre of the circular trajectory.
Hence, Direction of acceleration keeps changing as particle moves.
Step 3: Find angular momentum.
Formula used : →L=m(→r×→v)
As mass of particle, radius of the circle and speed is constant, so the magnitude of the angular momentum will be constant.
As Velocity of the particle is directed tangent to the circle or perpendicular to the radius vector. So, direction of angular momentum is perpendicular to the plane containing →r and →v. (Which is constant)
Hence, angular momentum is constant.
Final answer : (a),(b),(c)
Definition: Uniform circular motion: It can be described as motion of an object in a circle at a constant speed.
Step 1: Find the speed and velocity of the particle.
when an object moves in a circle, it is constantly changing its direction. At all instances, the object is moving tangent to the circle. Since the direction of the velocity vector is the same as the direction of the object's motion, the velocity vector is directed tangent to the circle or perpendicular to the radius vector. As motion is uniform so, speed remains constant.
Step 2: Find the acceleration of the particle.
Hint: Tangential acceleration measure how the tangential velocity of a point in circular motion changes with time.
As in uniform circular motion tangential speed of the particle remains constant. Therefore, tangential acceleration of the particle will be zero.
Particle will have only centripetal acceleration (as it moves in a circle), and direction of centripetal acceleration is always towards the centre of the circular trajectory.
Hence, Direction of acceleration keeps changing as particle moves.
Step 3: Find angular momentum.
Formula used : →L=m(→r×→v)
As mass of particle, radius of the circle and speed is constant, so the magnitude of the angular momentum will be constant.
As Velocity of the particle is directed tangent to the circle or perpendicular to the radius vector. So, direction of angular momentum is perpendicular to the plane containing →r and →v. (Which is constant)
Hence, angular momentum is constant.
Final answer : (a),(b),(c)
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