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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