Question

A uniform rod of mass M and length L is pivoted at one end. The rod is left to freely rotate under the influence of its own weight. Find its angular acceleration α when it makes an angle 30° with the vertical axis. Solve for M=1 Kg, L=1 m, take g=10 m s-2. Hint: Find the center of mass for the rod, and calculate the torque, then apply Newton as τ= Ι·α

Answer #1

As we know that the weight Mg of the rod will act at the centre of mass that is L/2 distance from the pivot end.

Consider the following diagram .

Now torque about the pivot end = Mg*(L/2)Sin30 = (1*10)*(1/2)Sin30
= 2.5 Nm

We know that

torque(T) = I

where I is the moment of inertia = ML^{2}/3 =
(1)*1^{2} /3 = 0.333 kg-m^{2}

and is the angular acceleration

Now

T = I

2.5 = 0.333*

= 7.5 rad/s^{2}

A uniform rod of mass M and length L is pivoted at one end. The
rod is left to freely rotate under the influence of its own weight.
Find its angular acceleration α when it makes an angle 30° with the
vertical axis. Solve for M=1 Kg, L=1 m, take g=10 m s-2. Your
answer in X.X rad s-2. Hint: Find the center of mass for the rod,
and calculate the torque, then apply Newton as τ= Ι·α

A homogeneous rod of length L=1.47 mL=1.47 m and mass m=4.43
kgm=4.43 kg is pivoted about one end. It starts at an angle of
θ=27.8 ∘θ=27.8 ∘ with the vertical as shown in Figure
1. You may find it useful to use I=13mL2I=13mL2 for a rod
pivoted about one end. The rod has just been released from rest at
θ.
1) What is the magnitude of the torque acting on the rod in this
position?
2) What is the angular...

A stick of mass M and length L is pivoted at one end. A
small mass m<M is attached to the right-hand end of the stick.
The stick is held horizontally and released from rest.
Given that the rotational inertia of a uniform rod
pivoted around one end is 1/3ML^2, determine the rotational inertia
of the described system.
Calculate the angular velocity of the system when it
reaches a vertical position. You cannot use rotational kinematics
here because angular acceleration...

The uniform thin rod in the figure below has mass M =
2.00 kg and length L = 2.87 m and is free to rotate on a
frictionless pin. At the instant the rod is released from rest in
the horizontal position, find the magnitude of the rod's angular
acceleration, the tangential acceleration of the rod's center of
mass, and the tangential acceleration of the rod's free end.
HINT
An illustration shows the horizontal initial position and
vertical final position...

(PLEASE COMPLETE ALL PARTS OF THE QUESTION)
A uniform thin rod of mass m = 2.9 kg and
length L = 1.9 m can rotate about an axle through its
center. Four forces are acting on it as shown in the figure. Their
magnitudes are F1 = 5.5 N,
F2 = 2.5 N, F3 = 11 N and
F4 = 19.5 N. F2 acts a
distance d = 0.23 m from the center of mass.
A) Calculate the magnitude τ1...

A uniform thin rod of length 0.56 m and mass 3.2 kg can rotate
in a horizontal plane about a vertical axis through its center. The
rod is at rest when a 3.5 g bullet traveling in the rotation plane
is fired into one end of the rod. As viewed from above, the
bullet's path makes angle θ = 60° with the rod. If the
bullet lodges in the rod and the angular velocity of the rod is
12.0 rad/s...

A uniform thin rod of length 0.45 m and mass 6.5 kg can rotate
in a horizontal plane about a vertical axis through its center. The
rod is a rest when a 3.0-g bullet traveling in the horizontal plane
of the rod is fired into one end of the rod. As viewed from above,
the direction of the bullet velocity makes an angle of 60° with the
rod (see the figure). If the bullet lodges in the rod and the...

A 150 g uniform rod of length 3.0 m is pivoted about one
end. What would be the angular acceleration due to gravity if the
rod were held horizontally and released from rest?

A rod with length L and mass M hangs vertically on a
frictionless, horizontal axel passing through its center. A ball of
mass m traveling horizontally at speed v0 hits and
sticks to the very bottom tip of the rod. To what maximum angle,
measured from vertical, does the rod, with the attached ball,
rotate? Answer in terms m, M, v0, L, and g.

thin rod of mass Mandlength Has a fixed rotation axis a distance
L/6 from one end.(a) Using the parallel-axis theorem, find the
moment of inertia of the roundabouts rotation axis. (b) Suppose the
rod is held horizontally at rest and then released. Draw a
free-body diagram of the rod at the moment of its release, and find
its angular acceleration atthis moment. (Remember that gravity acts
at the rod’scenter.)(c) Find the angular velocity of the rod as it
swings through...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 28 minutes ago

asked 59 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago