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The above figure shows a circular disc of 1kg mass and 0.2 m radius undergoing unconstrained planar motion under the action of two forces as shown. The magnitude of angular acceleration a of the disc is (a) 50 rad/s2 (b) 100 rad/s2 (c) 25 rad/s2 (d) 20 rad/s2?
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The above figure shows a circular disc of 1kg mass and 0.2 m radius un...
Angular acceleration is the rate at which the angular velocity of an object changes with time. It is given by the formula:
a = α * r
Where a is the angular acceleration, α is the angular acceleration, and r is the radius of the circular disc.
In this case, the disc is undergoing unconstrained planar motion, which means it is free to move in any direction in the plane. The two forces acting on the disc are shown in the figure. Let's analyze each force separately.
1. Force F1:
The force F1 is acting tangentially to the disc, causing a torque (τ1) on the disc. The magnitude of the torque is given by the formula:
τ1 = F1 * r
Since the force F1 is acting tangentially, it will cause the disc to rotate. The torque τ1 will produce an angular acceleration (α1) in the disc. The magnitude of the angular acceleration is given by the formula:
α1 = τ1 / I
Where I is the moment of inertia of the disc. For a circular disc, the moment of inertia is given by the formula:
I = (1/2) * m * r^2
Where m is the mass of the disc and r is the radius of the disc.
2. Force F2:
The force F2 is acting radially towards the center of the disc. Since the force is acting radially, it will not produce any torque on the disc. Therefore, it will not contribute to the angular acceleration of the disc.
Now let's calculate the magnitude of the angular acceleration:
α = α1
Since the force F1 is the only force producing a torque on the disc, it will be responsible for the angular acceleration.
Substituting the values into the formulas:
τ1 = F1 * r
I = (1/2) * m * r^2
α1 = τ1 / I
We can see that the radius (r) and mass (m) of the disc are given in the figure. We need to determine the magnitude of the force F1 to calculate the angular acceleration.
Unfortunately, the figure does not provide any information about the force F1. Without knowing the magnitude of the force F1, we cannot determine the magnitude of the angular acceleration (α) of the disc. Therefore, the answer cannot be determined based on the given information.
Option (e) "Cannot be determined"
a = α * r
Where a is the angular acceleration, α is the angular acceleration, and r is the radius of the circular disc.
In this case, the disc is undergoing unconstrained planar motion, which means it is free to move in any direction in the plane. The two forces acting on the disc are shown in the figure. Let's analyze each force separately.
1. Force F1:
The force F1 is acting tangentially to the disc, causing a torque (τ1) on the disc. The magnitude of the torque is given by the formula:
τ1 = F1 * r
Since the force F1 is acting tangentially, it will cause the disc to rotate. The torque τ1 will produce an angular acceleration (α1) in the disc. The magnitude of the angular acceleration is given by the formula:
α1 = τ1 / I
Where I is the moment of inertia of the disc. For a circular disc, the moment of inertia is given by the formula:
I = (1/2) * m * r^2
Where m is the mass of the disc and r is the radius of the disc.
2. Force F2:
The force F2 is acting radially towards the center of the disc. Since the force is acting radially, it will not produce any torque on the disc. Therefore, it will not contribute to the angular acceleration of the disc.
Now let's calculate the magnitude of the angular acceleration:
α = α1
Since the force F1 is the only force producing a torque on the disc, it will be responsible for the angular acceleration.
Substituting the values into the formulas:
τ1 = F1 * r
I = (1/2) * m * r^2
α1 = τ1 / I
We can see that the radius (r) and mass (m) of the disc are given in the figure. We need to determine the magnitude of the force F1 to calculate the angular acceleration.
Unfortunately, the figure does not provide any information about the force F1. Without knowing the magnitude of the force F1, we cannot determine the magnitude of the angular acceleration (α) of the disc. Therefore, the answer cannot be determined based on the given information.
Option (e) "Cannot be determined"
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The above figure shows a circular disc of 1kg mass and 0.2 m radius undergoing unconstrained planar motion under the action of two forces as shown. The magnitude of angular acceleration a of the disc is (a) 50 rad/s2 (b) 100 rad/s2 (c) 25 rad/s2 (d) 20 rad/s2?
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The above figure shows a circular disc of 1kg mass and 0.2 m radius undergoing unconstrained planar motion under the action of two forces as shown. The magnitude of angular acceleration a of the disc is (a) 50 rad/s2 (b) 100 rad/s2 (c) 25 rad/s2 (d) 20 rad/s2? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The above figure shows a circular disc of 1kg mass and 0.2 m radius undergoing unconstrained planar motion under the action of two forces as shown. The magnitude of angular acceleration a of the disc is (a) 50 rad/s2 (b) 100 rad/s2 (c) 25 rad/s2 (d) 20 rad/s2? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The above figure shows a circular disc of 1kg mass and 0.2 m radius undergoing unconstrained planar motion under the action of two forces as shown. The magnitude of angular acceleration a of the disc is (a) 50 rad/s2 (b) 100 rad/s2 (c) 25 rad/s2 (d) 20 rad/s2?.
The above figure shows a circular disc of 1kg mass and 0.2 m radius undergoing unconstrained planar motion under the action of two forces as shown. The magnitude of angular acceleration a of the disc is (a) 50 rad/s2 (b) 100 rad/s2 (c) 25 rad/s2 (d) 20 rad/s2? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The above figure shows a circular disc of 1kg mass and 0.2 m radius undergoing unconstrained planar motion under the action of two forces as shown. The magnitude of angular acceleration a of the disc is (a) 50 rad/s2 (b) 100 rad/s2 (c) 25 rad/s2 (d) 20 rad/s2? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The above figure shows a circular disc of 1kg mass and 0.2 m radius undergoing unconstrained planar motion under the action of two forces as shown. The magnitude of angular acceleration a of the disc is (a) 50 rad/s2 (b) 100 rad/s2 (c) 25 rad/s2 (d) 20 rad/s2?.
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