Class 11 Exam > Class 11 Questions > The angular speed of a wheel of radius 0.50 m...
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The angular speed of a wheel of radius 0.50 m moving with the speed of 20 m/s is:
- a)40 radian/s
- b)10 radian/s
- c)30 radian/s
- d)20 radian/s
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The angular speed of a wheel of radius 0.50 m moving with the speed of...
Radius r = 0.5 m
Speed, v = 20 m/s
We know,
v = r ω
where,
ω = angular velocity
20 = 0.5 x ω
ω = 20/0.5 = 40 rad/sec
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The angular speed of a wheel of radius 0.50 m moving with the speed of...
Angular speed is defined as the rate at which an object rotates or moves around a fixed point. It is measured in radians per second (rad/s). To find the angular speed of a wheel, we need to relate the linear speed of the wheel to its angular speed.
Given:
Radius of the wheel (r) = 0.50 m
Linear speed of the wheel (v) = 20 m/s
We can use the formula for linear speed and angular speed to find the angular speed of the wheel:
Linear speed (v) = radius (r) × angular speed (ω)
To find ω, we rearrange the formula:
Angular speed (ω) = Linear speed (v) / radius (r)
Substituting the given values:
ω = 20 m/s / 0.50 m
Simplifying the expression:
ω = 40 rad/s
Therefore, the correct answer is option A: 40 radian/s.
Summary:
The angular speed of the wheel can be found by dividing the linear speed of the wheel by its radius. In this case, the angular speed is 40 radian/s.
Given:
Radius of the wheel (r) = 0.50 m
Linear speed of the wheel (v) = 20 m/s
We can use the formula for linear speed and angular speed to find the angular speed of the wheel:
Linear speed (v) = radius (r) × angular speed (ω)
To find ω, we rearrange the formula:
Angular speed (ω) = Linear speed (v) / radius (r)
Substituting the given values:
ω = 20 m/s / 0.50 m
Simplifying the expression:
ω = 40 rad/s
Therefore, the correct answer is option A: 40 radian/s.
Summary:
The angular speed of the wheel can be found by dividing the linear speed of the wheel by its radius. In this case, the angular speed is 40 radian/s.
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