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a paticle is moving in a circular path of radius 10m with constant speed 20m/s its change in its velocity when its radius vector turned 60 degresz is
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Explanation of Change in Velocity of a Particle Moving in a Circular Path
When a particle moves in a circular path, it undergoes constant acceleration towards the center of the circle. This acceleration is known as centripetal acceleration.
Calculating Centripetal Acceleration
The formula for centripetal acceleration is:
ac = v2/r
Where v is the velocity of the particle and r is the radius of the circular path.
In this case, the velocity of the particle is constant at 20m/s and the radius of the circular path is 10m. Therefore, the centripetal acceleration is:
ac = (20 m/s)2/10m = 40 m/s2
Change in Velocity
When the radius vector of the particle turns by an angle of 60 degrees, the direction of the velocity vector changes. This change in direction results in a change in the velocity of the particle.
The magnitude of the change in velocity can be calculated using the following formula:
Δv = acΔt
Where Δt is the time taken for the radius vector to turn by an angle of 60 degrees.
The time taken for the radius vector to turn by an angle of 60 degrees can be calculated using the formula:
Δt = Δθ/ω
Where Δθ is the change in angle and ω is the angular velocity of the particle.
Since the particle is moving at a constant speed, its angular velocity can be calculated using the formula:
ω = v/r
Therefore, ω = 20m/s / 10m = 2 rad/s
Substituting the values, we get:
Δt = (60 degrees)(π/180) / 2 rad/s = π/6 seconds
Substituting the value of Δt in the formula for change in velocity, we get:
Δv = (40 m/s2)(π/6 seconds) = 20π m/s
Conclusion
Therefore, the change in velocity of the particle when its radius vector turns by an angle of 60 degrees is 20π m/s.
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a paticle is moving in a circular path of radius 10m with constant speed 20m/s its change in its velocity when its radius vector turned 60 degresz is
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a paticle is moving in a circular path of radius 10m with constant speed 20m/s its change in its velocity when its radius vector turned 60 degresz is for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about a paticle is moving in a circular path of radius 10m with constant speed 20m/s its change in its velocity when its radius vector turned 60 degresz is covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for a paticle is moving in a circular path of radius 10m with constant speed 20m/s its change in its velocity when its radius vector turned 60 degresz is.
a paticle is moving in a circular path of radius 10m with constant speed 20m/s its change in its velocity when its radius vector turned 60 degresz is for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about a paticle is moving in a circular path of radius 10m with constant speed 20m/s its change in its velocity when its radius vector turned 60 degresz is covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for a paticle is moving in a circular path of radius 10m with constant speed 20m/s its change in its velocity when its radius vector turned 60 degresz is.
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