Angular speed and linear speed

In summary, the ball has a radius of 4 cm and moves at 5000 rpm. The angular speed is calculated to be 166.67∏°/sec. The period of rotation is 0.012 seconds. No additional information is provided.
  • #1
imy786
322
0

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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  • #3
1 rev = 2∏ radians = 360° ; be careful with your units.
You might as well say that omega = 523.6 rad/sec.
 
  • #4
Find the period of rotation

T = 2 ∏ / omega = 2∏/523.6 = 0.012 seconds
 
  • #5
is this correct?
 
  • #6
why isn't anyone responding?
 

1. What is the difference between angular speed and linear speed?

Angular speed is the rate at which an object rotates around a fixed axis, while linear speed is the rate at which an object moves along a straight line. Angular speed is measured in radians per second, while linear speed is measured in meters per second.

2. How are angular speed and linear speed related?

Angular speed and linear speed are related by the equation v = ωr, where v is linear speed, ω is angular speed, and r is the distance from the object to the axis of rotation. This means that as angular speed increases, linear speed also increases.

3. What is the unit of measurement for angular speed and linear speed?

Angular speed is measured in radians per second (rad/s), while linear speed is measured in meters per second (m/s).

4. How can I calculate angular speed and linear speed?

To calculate angular speed, divide the angular displacement (in radians) by the time taken to make that displacement. To calculate linear speed, divide the distance traveled (in meters) by the time taken to travel that distance.

5. In what situations would I use angular speed and linear speed?

Angular speed is typically used to describe the speed of objects that are rotating, such as wheels, gears, and planets. Linear speed is used to describe the speed of objects that are moving along a straight path, such as cars, runners, and projectiles.

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