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?

Solutions

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

Next > < Previous

Related Solutions

A Wheel initially rotating at an angular velocity of 15.0 rad/s is decelerating at a rate...

A Wheel initially rotating at an angular velocity of 15.0 rad/s is decelerating at a rate of 2.0 rad/s². How many revolutions will the wheel make before coming to rest?

A wheel rotates with a constant angular acceleration of 3.0 rad/. If the angular speed of...

A wheel rotates with a constant angular acceleration of 3.0 rad/. If the angular speed of the wheel is 2 rad/s at t = 0, through what angular displacement does the wheel rotate in 2 s? 10 rad. 6 rad. 15 rad. 4 rad. 12 rad. Based on question number 3, through how many revolutions has the wheel turned during this time interval? 4 rev. 3 rev. 1.6 rev. 5 rev. 2 rev. Based on question number 3, what is...

Two spheres are each rotating at an angular speed of 24.6 rad/s about axes that pass...

Two spheres are each rotating at an angular speed of 24.6 rad/s about axes that pass through their centers. Each has a radius of 0.440 m and a mass of 1.65 kg. However, one is solid and the other is a thin-walled spherical shell. Suddenly, a net external torque due to friction (magnitude = 0.230 N · m) begins to act on each sphere and slows the motion down. How long does it take (a) the solid sphere and (b)...

A rotating wheel requires 2.97-s to rotate through 37.0 revolutions. Its angular speed at the end...

A rotating wheel requires 2.97-s to rotate through 37.0 revolutions. Its angular speed at the end of the 2.97-s interval is 97.0 rad/s. What is the constant angular acceleration of the wheel? _____ rad/s2

The balance wheel of a watch oscillates with angular amplitude 1.2π rad and period 0.70 s....

The balance wheel of a watch oscillates with angular amplitude 1.2π rad and period 0.70 s. Find (a) the maximum angular speed of the wheel, (b) the angular speed of the wheel at displacement 1.2π/2 rad, and (c) the magnitude of the angular acceleration at displacement 1.2π/4 rad.

what is the angular displacement of the wheel between t = 5 s and t = 15 s

(Figure 1) shows the angular position of a potter's wheel. Part A What is the angular displacement of the wheel between t = 5 s and t = 15 s? Express your answer in radians. Part B What is the angular velocity of the wheel at 15 s? Express your answer in radians per second. Part C What is the maximum speed of a point on the outside of the wheel 15 cm from the axle? Express

1. A flywheel is initially rotating at 30 rad/s and has a constant angular acceleration. After...

1. A flywheel is initially rotating at 30 rad/s and has a constant angular acceleration. After 8.0 s it has rotated through 460 rad. Its angular acceleration in rad/s is: 2.Ten seconds after an electric fan is turned on, the fan rotates at 6000 rev/min. Its average angular acceleration in rad/s2 is: 3.The rotational inertia of a disk about its axis is 0.70 kgˑm2. When a 2.0-kg weight is added to its rim, 0.50 m from the axis, the rotational...

A wheel, released from rest, is rotating with constant angular acceleration. After 8.0 seconds, its speed...

A wheel, released from rest, is rotating with constant angular acceleration. After 8.0 seconds, its speed reaches to 12 rev/sec (a) what is its angular acceleration? (b) Through what angle has the wheel turned? (c) How many revolutions has it completed in 8.0 second?

The Earth has an angular speed of 7.272·10-5 rad/s in its rotation. Find the new angular...

The Earth has an angular speed of 7.272·10-5 rad/s in its rotation. Find the new angular speed if an asteroid (m = 3.91·1022 kg) hits the Earth while traveling at a speed of 2.87·103m/s (assume the asteroid is a point mass compared to the radius of the Earth) in each of the following cases: a) The asteroid hits the Earth dead center. b) The asteroid hits the Earth nearly tangentially in the direction of Earth's rotation. c) The asteroid hits...

The Earth has an angular speed of 7.272·10-5 rad/s in its rotation. Find the new angular...

The Earth has an angular speed of 7.272·10-5 rad/s in its rotation. Find the new angular speed if an asteroid (m = 4.87·1022 kg) hits the Earth while traveling at a speed of 4.93·103 m/s (assume the asteroid is a point mass compared to the radius of the Earth) in each of the following cases: a) The asteroid hits the Earth dead center. b) The asteroid hits the Earth nearly tangentially in the direction of Earth's rotation. c) The asteroid...

Subjects