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A disc of radius 1 m is rotating about central axis with angular velocity 2 rad/s. If a point P Lying on its circumference as shown is moving with velocity 4j m/s, then velocity of centre of disc is (1) (2i 4j) m/s (2) (4i 2i) m/s (3) (-2i 4j) m/s (4) (2i-4j) m/s?
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A disc of radius 1 m is rotating about central axis with angular veloc...
v = rw
here v =velocity
r=radius
w= angular velocity
for center radius will be 0
hence velocity also be 0
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A disc of radius 1 m is rotating about central axis with angular veloc...
Given:
- Radius of the disc, r = 1 m
- Angular velocity, ω = 2 rad/s
- Velocity of point P, vP = 4j m/s
To find:
Velocity of the center of the disc
Explanation:
The velocity of any point on a rotating disc can be divided into two components:
1. Tangential velocity: This component is in the direction of the tangent to the point's path on the disc.
2. Radial velocity: This component is in the direction perpendicular to the tangent and points towards the center of the disc.
Since point P is moving with a velocity of 4j m/s, it means that only the tangential velocity component is present.
Let's denote the tangential velocity component as vT.
Deriving the formula:
The tangential velocity of a point on a rotating disc can be calculated using the formula:
vT = rω
where r is the distance of the point from the axis of rotation and ω is the angular velocity.
In this case, r = 1 m and ω = 2 rad/s, so the tangential velocity vT is:
vT = 1 * 2 = 2 m/s
Calculating the velocity of the center of the disc:
The velocity of the center of the disc can be found by adding the tangential velocity of point P to the radial velocity of point P.
Since the point P is on the circumference of the disc, its radial velocity component is equal to the tangential velocity component, but in the opposite direction. Let's denote the radial velocity component as vR.
Therefore, vR = -2j m/s
The velocity of the center of the disc is the vector sum of the tangential velocity and the radial velocity:
vCenter = vT + vR
Substituting the values, we get:
vCenter = 2i + (-2j)
vCenter = 2i - 2j
Answer:
The velocity of the center of the disc is (2i - 2j) m/s. Therefore, the correct option is (4) (2i - 4j) m/s.
- Radius of the disc, r = 1 m
- Angular velocity, ω = 2 rad/s
- Velocity of point P, vP = 4j m/s
To find:
Velocity of the center of the disc
Explanation:
The velocity of any point on a rotating disc can be divided into two components:
1. Tangential velocity: This component is in the direction of the tangent to the point's path on the disc.
2. Radial velocity: This component is in the direction perpendicular to the tangent and points towards the center of the disc.
Since point P is moving with a velocity of 4j m/s, it means that only the tangential velocity component is present.
Let's denote the tangential velocity component as vT.
Deriving the formula:
The tangential velocity of a point on a rotating disc can be calculated using the formula:
vT = rω
where r is the distance of the point from the axis of rotation and ω is the angular velocity.
In this case, r = 1 m and ω = 2 rad/s, so the tangential velocity vT is:
vT = 1 * 2 = 2 m/s
Calculating the velocity of the center of the disc:
The velocity of the center of the disc can be found by adding the tangential velocity of point P to the radial velocity of point P.
Since the point P is on the circumference of the disc, its radial velocity component is equal to the tangential velocity component, but in the opposite direction. Let's denote the radial velocity component as vR.
Therefore, vR = -2j m/s
The velocity of the center of the disc is the vector sum of the tangential velocity and the radial velocity:
vCenter = vT + vR
Substituting the values, we get:
vCenter = 2i + (-2j)
vCenter = 2i - 2j
Answer:
The velocity of the center of the disc is (2i - 2j) m/s. Therefore, the correct option is (4) (2i - 4j) m/s.
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A disc of radius 1 m is rotating about central axis with angular veloc...
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A disc of radius 1 m is rotating about central axis with angular velocity 2 rad/s. If a point P Lying on its circumference as shown is moving with velocity 4j m/s, then velocity of centre of disc is (1) (2i 4j) m/s (2) (4i 2i) m/s (3) (-2i 4j) m/s (4) (2i-4j) m/s?
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A disc of radius 1 m is rotating about central axis with angular velocity 2 rad/s. If a point P Lying on its circumference as shown is moving with velocity 4j m/s, then velocity of centre of disc is (1) (2i 4j) m/s (2) (4i 2i) m/s (3) (-2i 4j) m/s (4) (2i-4j) m/s? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A disc of radius 1 m is rotating about central axis with angular velocity 2 rad/s. If a point P Lying on its circumference as shown is moving with velocity 4j m/s, then velocity of centre of disc is (1) (2i 4j) m/s (2) (4i 2i) m/s (3) (-2i 4j) m/s (4) (2i-4j) m/s? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A disc of radius 1 m is rotating about central axis with angular velocity 2 rad/s. If a point P Lying on its circumference as shown is moving with velocity 4j m/s, then velocity of centre of disc is (1) (2i 4j) m/s (2) (4i 2i) m/s (3) (-2i 4j) m/s (4) (2i-4j) m/s?.
A disc of radius 1 m is rotating about central axis with angular velocity 2 rad/s. If a point P Lying on its circumference as shown is moving with velocity 4j m/s, then velocity of centre of disc is (1) (2i 4j) m/s (2) (4i 2i) m/s (3) (-2i 4j) m/s (4) (2i-4j) m/s? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A disc of radius 1 m is rotating about central axis with angular velocity 2 rad/s. If a point P Lying on its circumference as shown is moving with velocity 4j m/s, then velocity of centre of disc is (1) (2i 4j) m/s (2) (4i 2i) m/s (3) (-2i 4j) m/s (4) (2i-4j) m/s? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A disc of radius 1 m is rotating about central axis with angular velocity 2 rad/s. If a point P Lying on its circumference as shown is moving with velocity 4j m/s, then velocity of centre of disc is (1) (2i 4j) m/s (2) (4i 2i) m/s (3) (-2i 4j) m/s (4) (2i-4j) m/s?.
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