Question

In: Math

A wheel of radius 8 inches is rotating 15°/s. What is the linear speed v, the angular speed in RPM, and the angular speed in rad/s?

Expert Solution

The radius of a wheel is equal to 8 inches and angular speed is equal to 15 degrees per second. The angular speed of the wheel is 15 degrees per second. Convert the angular speed in radians per second as follows:

15 degrees/second × 2π radians/360 degrees = 30π/360 rad/sec

= π/12 rad/sec

As 1 minute is equal is 60 seconds, the angular speed in converted into rad/min as follows:

π/12 rad/sec = (π/12 rad/sec) × (60 sec/1min)

= π/2 × 60 rad/min

= 5π rad/min

The number of revolutions taken by wheel in 1 minute will be computed as follows:

5π × 1/2π = 2.5 RPM

Consider the relation between angular speed (w) and linear speed (v),

v = rw

Substitute r = 8 in and w = π/12 rad/s, the linear speed of the wheel will be,

v = 8 × π/12

= 2.0943951…

≈ 2.09 in/s

Therefore, the linear speed of the wheel is approximately 2.09 in/s.

Junaid answered 1 year ago

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