Question

A wheel is being held in the air and rotates about a fixed axle. At time t = 0 the wheel is spinning with an angular velocity ?i= 327 rad/sec in the counter-clockwise direction. The position of a spot on the wheel is at an angle ?i=0 at the time t = 0.

At t = 0 a constant clockwise torque is applied to the wheel such that there is a constant clockwise angular acceleration ?=? 3.50 rad/s2.

How long will it take for the wheel to turn back to where the spot on the wheel is at ?f=0?

Give your answer in Seconds to at least three digits to avoid being counted incorrect due to rounding.

**NOTE**: The angle in this problem is not limited
to the values 0???2?. The angle can be larger than 2?, indicating
that the wheel has gone around more than one revolution. For
example, if the wheel turns through three revolutions, ?=6?. Thus
?f=0 implies that wheel may have turned several revolutions
counter-clockwise and then rotated BACK the same number of
revolutions clockwise.

Answer #1

A wheel rotates with a constant angular acceleration of 3.00
rad/s2. If the angular speed of the wheel is 2.50 rad/s at t = 0,
how many revolutions has the wheel gone through after 2.90 s?

PRACTICE IT
A wheel rotates with a constant angular acceleration of 3.25
rad/s2. Assume the angular speed of the wheel is 2.20
rad/s at ti = 0.
(a) Through what angle does the wheel rotate between t
= 0 and t = 2.00 s? Give your answer in radians and
revolutions.
___________ rad
___________ rev
(b) What is the angular speed of the wheel at t = 2.00
s?
___________rad/s
(c) What angular displacement (in revolutions) results while the
angular...

A wheel rotates with a constant angular acceleration of 3.90
rad/s2. Assume the angular speed of the wheel is 2.05
rad/s at ti = 0.
(a) Through what angle does the wheel rotate between t
= 0 and t = 2.00 s? Give your answer in radians and
revolutions.
rad?
rev?
(b) What is the angular speed of the wheel at t = 2.00
s?
rad/s?
(c) What angular displacement (in revolutions) results while the
angular speed found in part...

A 0.60 m radius wheel starting from rest rotates through an
angle θ. If it is accelerating at a constant angular acceleration
of 2.40 rad/s2, determine
(a) the angular
velocity in rad/s of the wheel at the end of a 5.00 second
interval.
(b) how many
revolutions has the wheel rotated by the end of the 5.00 second
interval.

A wheel rotates with a constant angular acceleration of 3.90
rad/s2. Assume the angular speed of the wheel is 1.55
rad/s at ti = 0.
(a) Through what angle does the wheel rotate between t
= 0 and t = 2.00 s? Give your answer in radians and
revolutions.
___________rad
___________ rev
(b) What is the angular speed of the wheel at t = 2.00
s?
__________rad/s
(c) What angular displacement (in revolutions) results while the
angular speed found in...

A wheel 2.20 m in diameter lies in a vertical plane and rotates
about its central axis with a constant angular acceleration of 4.10
rad/s2. The wheel starts at rest at t = 0, and
the radius vector of a certain point P on the rim makes an
angle of 57.3° with the horizontal at this time. At t =
2.00 s, find the following.
(a) the angular speed of the wheel
(b) the tangential speed of the point P...

A wheel 1.55 m in
diameter lies in a vertical plane and rotates about its central
axis with a constant angular acceleration of 3.65
rad/s2. The wheel starts at rest at t
= 0, and the radius vector of a certain
point P on the rim makes
an angle of 57.3

A wheel 1.50 m in diameter lies in a vertical plane and rotates
about its central axis with a constant angular acceleration of 3.95
rad/s2. The wheel starts at rest at t = 0, and
the radius vector of a certain point P on the rim makes an
angle of 57.3° with the horizontal at this time. At t =
2.00 s, find the following.
(a) the angular speed of the wheel
rad/s
(b) the tangential speed of the point...

A wheel 1.65 m in diameter lies in a vertical plane and rotates
about its central axis with a constant angular acceleration of 4.35
rad/s2. The wheel starts at rest at t = 0, and
the radius vector of a certain point P on the rim makes an
angle of 57.3° with the horizontal at this time. At t =
2.00 s, find the following.
(a) the angular speed of the wheel
(b) the tangential speed of the point P...

A wheel starts from rest and rotates about its axis with
constant angular acceleration. After 5.7 s have elapsed, it has
rotated through an angle of 20 radians. What is the angular
acceleration of the wheel? What is the angular velocity when the
time t = 5.7 s? What is the centripetal acceleration of a point on
the wheel a distance r = 0.35 m from the axis at t = 5.7 s?

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