Question

In: Physics

A helicopter propeller blade starts from rest and experiences a constant angular acceleration of 14.0 rad/s2....

A helicopter propeller blade starts from rest and experiences a constant angular acceleration of 14.0 rad/s2. Find the speed of a point on the blade 5.60 m from the axis of rotation when the blade has completed 13 revolutions.

Expert Solution

Using equation of rotational motion (iii), we have

² = _i² + 2

where, _i = initial angular speed of blade = 0 rad/s

= constant angular acceleration = 14 rad/s²

= angular distance completed by blade = 13 rev = 81.6 rad

then, we get

² = (2) (14 rad/s²) (81.6 rad)

= 2284.8 rad²/s²

= 47.8 rad/s

Therefore, the speed of a point on the blade from the axis of rotation which will be given by -

v = r

v = [(5.60 m) (47.8 rad/s)]

v = 267.6 m/s

genius_generous answered 7 months ago

A wheel, starting from rest, rotates with a constant angular acceleration of 1.40 rad/s2. During a...

A wheel, starting from rest, rotates with a constant angular acceleration of 1.40 rad/s2. During a certain 6.00 s interval, it turns through 36.6 rad. (a) How long had the wheel been turning before the start of the 6.00 s interval? (b) What was the angular velocity of the wheel at the start of the 6.00 s interval?

A 41.0-cm diameter disk rotates with a constant angular acceleration of 2.90 rad/s2. It starts from...

A 41.0-cm diameter disk rotates with a constant angular acceleration of 2.90 rad/s2. It starts from rest at t = 0, and a line drawn from the center of the disk to a point P on the rim of the disk makes an angle of 57.3° with the positive x-axis at this time. (a) At t = 2.49 s, find the angular speed of the wheel. (b) At t = 2.49 s, find the magnitude of the linear velocity AND...

A 45.3-cm diameter disk rotates with a constant angular acceleration of 2.30 rad/s2. It starts from...

A 45.3-cm diameter disk rotates with a constant angular acceleration of 2.30 rad/s2. It starts from rest at t = 0, and a line drawn from the center of the disk to a point P on the rim of the disk makes an angle of 57.3° with the positive x-axis at this time. (a) Find the angular speed of the wheel at t = 2.30 s 5.26 (correct) rad/s (b) Find the linear velocity and tangential acceleration of P at...

A 40.0-cm diameter disk rotates with a constant angular acceleration of 3.00 rad/s2. It starts from...

A 40.0-cm diameter disk rotates with a constant angular acceleration of 3.00 rad/s2. It starts from rest at t = 0, and a line drawn from the center of the disk to a point P on the rim of the disk makes an angle of 57.3° with the positive x-axis at this time. (a) At t = 2.45 s, find the angular speed of the wheel. (b) At t = 2.45 s, find the magnitude of the linear velocity and...

A wheel, starting from rest, has a constant angular acceleration of 0.1 rad/s2. In a 2.4-s...

A wheel, starting from rest, has a constant angular acceleration of 0.1 rad/s2. In a 2.4-s interval, it turns through an angle of 120 rad. How long has the wheel been in motion at the start of this 2.4-s interval?

A Ferris Wheel, starting from rest, undergoes a constant angular acceleration of 0.033 rad/s2 to get...

A Ferris Wheel, starting from rest, undergoes a constant angular acceleration of 0.033 rad/s2 to get to its final operating angular velocity of 0.24 rad/s. (a) How long does it take the Ferris Wheel to get to its operating angular velocity? (b) How many revolutions does it make during this time interval?

The drive propeller of a ship starts from rest and accelerates at 2.99 x 10-3 rad/s2...

The drive propeller of a ship starts from rest and accelerates at 2.99 x 10-3 rad/s2 for 2.86 x 103 s. For the next 1.90 x 103 s the propeller rotates at a constant angular speed. Then it decelerates at 2.61 x 10-3 rad/s2 until it slows (without reversing direction) to an angular speed of 2.31 rad/s. Find the total angular displacement of the propeller.

The drive propeller of a ship starts from rest and accelerates at 2.56 x 10-3 rad/s2...

The drive propeller of a ship starts from rest and accelerates at 2.56 x 10-3 rad/s2 for 2.48 x 103 s. For the next 1.47 x 103 s the propeller rotates at a constant angular speed. Then it decelerates at 2.80 x 10-3 rad/s2 until it slows (without reversing direction) to an angular speed of 2.88 rad/s. Find the total angular displacement of the propeller.

A merry-go-round rotates from rest with an angular acceleration of 1.11 rad/s2. How long does it...

A merry-go-round rotates from rest with an angular acceleration of 1.11 rad/s2. How long does it take to rotate through (a) the first 1.85 rev and (b) the next 1.85 rev? Please include an explanation

A dentist's drill starts from rest. After 3.20 s of constant angular acceleration it turns at...

A dentist's drill starts from rest. After 3.20 s of constant angular acceleration it turns at a rate of 3.00 ✕ 104 rev/min. (a) Find the drill's angular acceleration. rad/s2 (b) Determine the angle (in radians) through which the drill rotates during this period. rad