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Linear Speed Formula

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The physical distance travelled by a moving item is always measured by linear speed. As a result, the linear speed is measured in path length units per unit of time. For instance, a meter per second. When an item moves in a circular motion, the term linear refers to smoothing out the curve that the object travels alongside the circle. It yields a line that is the same length. As a result, the standard definition of speed is correct: distance divided by time.

Linear Speed

The distance between a point on a spinning object and the centre of rotation can be used to calculate its linear speed. The angular speed of an item is the angle it moves through in a given length of time. The angular speed will be expressed in radians per second (radian per second).

Given a complete circle, it has 2Ï€ radians. At a distance of r, or radius, from the rotation’s centre. The linear speed of a point on the object is thus equal to the angular speed multiplied by the distance r. Meters per second and meters per second is the unit of measurement.

Formula

V = ω × r

where,

  • ω = speed in radians/ sec.
  • r denotes the radius of the rotation

Sample Problems

Question 1. Find the linear speed of a point on a wheel given that its speed is 14 RPS and diameter is 4 m.

Solution:

ω = 14 RPS or, 87.96 radians per second

 r = 4/2 = 2 m

Since, V = ω × r

= 87.96 × 2

V = 175.92 m/s

Question 2. Find the linear speed of a point on a wheel given that its speed is 8 RPS and diameter is 4 m.

Solution:

ω = 14 RPS or, 87.96 radians per second

r = 8/2 = 4 m

Since, V = ω × r

= 87.96 × 4

V = 351.84 m/s

Question 3. Find the linear speed of a point on a wheel given that its speed is 5 RPS and diameter is 2 m.

Solution:

ω = 5 RPS or, 31.42 radians per second

r = 2/2 = 1 m

Since, V = ω × r

= 31.42 × 1

V = 31.42 m/s

Question 4. Find the linear speed of a point on a wheel given that its speed is 19 RPS and diameter is 80 m.

Solution:

ω = 14 RPS or, 1.9897 radians per second

r = 80/2 = 40 m

Since, V = ω × r

= 1.9897 × 40

V = 79.588 m/s

Question 5. Find the linear speed of a point on a wheel given that its speed is 7 RPS and diameter is 1 m.

Solution:

ω = 7 RPS or, 87.96 radians per second

r = 1/2 = 0.5 m

Since, V = ω × r

= 43.98 × 0.5

V = 21.99 m/s


Last Updated : 04 Feb, 2024
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