Question
A motorcycle wheel has a diamater of 19.5 inches and roots at 1050 revolutions per minute A. Find the angular speed in radians per minute, leave as exact value. Angular speed = θ/t B. Find the linear speed of the motorcycle in inches per minute. Linear speed = S/T
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Answer to a math question A motorcycle wheel has a diamater of 19.5 inches and roots at 1050 revolutions per minute A. Find the angular speed in radians per minute, leave as exact value. Angular speed = θ/t B. Find the linear speed of the motorcycle in inches per minute. Linear speed = S/T
Madelyn
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To find the angular speed in radians per minute, we need to find the angle in radians that the wheel covers in each revolution.
A. The circumference of a circle can be found using the formula:
C = πd
where C is the circumference and d is the diameter.
Given that the diameter of the motorcycle wheel is 19.5 inches, the circumference is:
C = π * 19.5
Next, we need to find the angle in radians covered in one revolution. Since a full circle has 2π radians, the angle in radians covered in one revolution is:
θ = 2π
Therefore, the angular speed in radians per minute is:
Angular speed = θ / t
where t is the time in minutes.
B. To find the linear speed of the motorcycle in inches per minute, we need to find the distance traveled in one revolution.
The distance traveled in one revolution is the circumference of the wheel, which we found in part A. Therefore, the linear speed can be calculated using the formula:
Linear speed = S / t
where S is the distance traveled and t is the time in minutes.
Given that the distance traveled in one revolution is the circumference of the wheel, the linear speed is:
Linear speed = π * 19.5
Therefore, the angular speed in radians per minute is:
Angular speed = 2π
And the linear speed in inches per minute is:
Linear speed = π * 19.5
Note: To evaluate the final answer, you can calculate the numerical values for π if needed.
Answer:
A. The angular speed in radians per minute is 2π.
B. The linear speed of the motorcycle in inches per minute is π * 19.5.
A. The circumference of a circle can be found using the formula:
C = πd
where C is the circumference and d is the diameter.
Given that the diameter of the motorcycle wheel is 19.5 inches, the circumference is:
C = π * 19.5
Next, we need to find the angle in radians covered in one revolution. Since a full circle has 2π radians, the angle in radians covered in one revolution is:
θ = 2π
Therefore, the angular speed in radians per minute is:
Angular speed = θ / t
where t is the time in minutes.
B. To find the linear speed of the motorcycle in inches per minute, we need to find the distance traveled in one revolution.
The distance traveled in one revolution is the circumference of the wheel, which we found in part A. Therefore, the linear speed can be calculated using the formula:
Linear speed = S / t
where S is the distance traveled and t is the time in minutes.
Given that the distance traveled in one revolution is the circumference of the wheel, the linear speed is:
Linear speed = π * 19.5
Therefore, the angular speed in radians per minute is:
Angular speed = 2π
And the linear speed in inches per minute is:
Linear speed = π * 19.5
Note: To evaluate the final answer, you can calculate the numerical values for π if needed.
Answer:
A. The angular speed in radians per minute is 2π.
B. The linear speed of the motorcycle in inches per minute is π * 19.5.
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