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The radius of a body moving in a circle with constant angular velocity is given by r = 4t2, with respect to time. What is the magnitude of the tangential velocity at t = 2s, if the angular velocity is 7 rad/s?
- a)112
- b)113
- c)56
- d)28
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The radius of a body moving in a circle with constant angular velocity...
Given Information
- Radius function: \( r(t) = 4t^2 \)
- Angular velocity: \( \omega = 7 \, \text{rad/s} \)
- Time: \( t = 2 \, \text{s} \)
Step 1: Calculate the Radius at \( t = 2 \, \text{s} \)
To find the radius at \( t = 2 \, \text{s} \):
- \( r(2) = 4(2^2) \)
- \( r(2) = 4(4) = 16 \, \text{m} \)
Step 2: Calculate the Tangential Velocity
The formula for tangential velocity (\( v \)) is given by:
- \( v = r \cdot \omega \)
Where:
- \( r \) is the radius
- \( \omega \) is the angular velocity
Now, substituting the known values:
- \( v = 16 \, \text{m} \cdot 7 \, \text{rad/s} \)
Step 3: Perform the Calculation
Calculating the tangential velocity:
- \( v = 16 \cdot 7 = 112 \, \text{m/s} \)
Conclusion
Therefore, the magnitude of the tangential velocity at \( t = 2 \, \text{s} \) is:
- **112 m/s**
The correct answer is option **A**.
- Radius function: \( r(t) = 4t^2 \)
- Angular velocity: \( \omega = 7 \, \text{rad/s} \)
- Time: \( t = 2 \, \text{s} \)
Step 1: Calculate the Radius at \( t = 2 \, \text{s} \)
To find the radius at \( t = 2 \, \text{s} \):
- \( r(2) = 4(2^2) \)
- \( r(2) = 4(4) = 16 \, \text{m} \)
Step 2: Calculate the Tangential Velocity
The formula for tangential velocity (\( v \)) is given by:
- \( v = r \cdot \omega \)
Where:
- \( r \) is the radius
- \( \omega \) is the angular velocity
Now, substituting the known values:
- \( v = 16 \, \text{m} \cdot 7 \, \text{rad/s} \)
Step 3: Perform the Calculation
Calculating the tangential velocity:
- \( v = 16 \cdot 7 = 112 \, \text{m/s} \)
Conclusion
Therefore, the magnitude of the tangential velocity at \( t = 2 \, \text{s} \) is:
- **112 m/s**
The correct answer is option **A**.
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Community Answer
The radius of a body moving in a circle with constant angular velocity...
The tangential velocity is given as v = ωr. At t = 2s, r = 16 units. The angular velocity is 7 rad/s. Hence, the tangential velocity, v = 7 x 16 = 112 units/s.
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The radius of a body moving in a circle with constant angular velocity is given by r = 4t2, with respect to time. What is the magnitude of the tangential velocity at t = 2s, if the angular velocity is 7 rad/s?a)112b)113c)56d)28Correct answer is option 'A'. Can you explain this answer?
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