How Do You Calculate the Angular and Linear Speed of a Ball?

AI Thread Summary
To calculate the angular speed of a ball moving at 5000 rpm with a radius of 4 cm, the angular speed is determined to be approximately 523.6 radians per second. The period of rotation is calculated using the formula T = 2π/ω, resulting in a period of about 0.012 seconds. The linear speed of a point on the outer edge of the ball can be derived from the angular speed and radius, while the linear acceleration can be calculated using the linear speed and the radius. The discussion highlights the importance of unit conversion and accuracy in calculations. Overall, the calculations for angular speed and period appear to be correct, but further clarification is sought on the linear speed and acceleration.
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Homework Statement



a ball moves at 5000 rpm (revolutions per minute). Their radius is 4 cm.

(i)Determine the angular speed in radians per second.

(ii) Find the period of rotation

(iii) Find the linear speed of a point on the outer ball

(iv) Find the linear acceleration of a point on the outer edge of the ball.

Homework Equations



angular speed = 2∏ / T

The Attempt at a Solution



(i)

r = 4cm = 0.04m
circumference = 2∏r = 0.08∏

1 rev = 2∏°
5000 rev/min = 5000 X 2∏° / min
10,000∏° / min
10,000∏° / min = 10,000∏° per 60 secs

10,000∏° / 60 = 166.67∏°/sec

angular speed = 166.67∏°/sec

is this correct for part (i)
 
Last edited:
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1 rev = 2∏ radians = 360° ; be careful with your units.
You might as well say that omega = 523.6 rad/sec.
 
Find the period of rotation

T = 2 ∏ / omega = 2∏/523.6 = 0.012 seconds
 
is this correct?
 
why isn't anyone responding?
 
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