# Physics woes - online course - Rotation

• epohxe
In summary: A solid disc has a frictiionless axle running through its center, allowing it to rotate about this axis. Radius is given. Find tangetial force required to accelerate the disc from rest to a given rotation rate in a given number of seconds.Given the mass of the disc, the amount of tension in the cable, and the distance the cable is from the center of the disc, the tangential force required to achieve the rotation is: F_t = ma = mg (where m is the mass of the disc, g is the gravitational force pulling on the disc, and g is the tension in the cable)
epohxe
Hi, i am glad i have found this site. I am taking an online physics course, the kind where you read the book, work the problems, and take the test. Needless to say it has been very hard on me. I must be really dense at physics because i have purchased supplemental books but to no avail. I have a few questions on rotation and would like to know if i can get a general outline as what to do. I am not posting specific homework problems, but just the general idea of them, so i may work them out myself.

#1. Given a rotation rate in rad/sec and an accelleration rate in rad/sec^2, find:
a. Rotation rate after a given time in seconds
b. Angular displacement in radians during that time.

#2. Someone is slinging a rock of given mass around his head. Knowing the length of the sling and rotation rate find tangetial velocity of mass, centripital acceleration of rock, and tension in rope.

#3. A wheel requires a given number of radians of rotation to accelerate from rest to a given angular rotation rate (in rad/sec). Find angular rate of acceleration, time to accelerate to given rotation rate, rotation rate after x seconds.

#4. A horizontal beam is attached to a frictionless hinge on a wall. Beam weight is given. A weight is placed on the beam at a given location. A VERTICAL cable supports the beam at the outer end. Find

tension in cable
x-component of force exerted on the beam by the wall
y-component of force exerted on the beam by the wall

(that VERTICAL cable is getting me)

#5. A solid disc has a frictiionless axle running through its center, allowing it to rotate about this axis. Radius is given. Find tangetial force required to accelerate the disc from rest to a given rotation rate in a given number of seconds.

These are the main problems i am having. Sorry if these seem somewhat easy to some people, but i do not even know where to start on some of them. Thanks to anyone who helps.

epohxe said:
Hi, i am glad i have found this site. I am taking an online physics course, the kind where you read the book, work the problems, and take the test. Needless to say it has been very hard on me. I must be really dense at physics because i have purchased supplemental books but to no avail. I have a few questions on rotation and would like to know if i can get a general outline as what to do. I am not posting specific homework problems, but just the general idea of them, so i may work them out myself.

#1. Given a rotation rate in rad/sec and an accelleration rate in rad/sec^2, find:
a. Rotation rate after a given time in seconds
b. Angular displacement in radians during that time.
Do you know the equation for angle displacement under constant conditions?
Hint: it looks a lot like the equations for linear displacement:

$$x(t) = x_0 + v_0t + \frac{1}{2} at^2$$

#2. Someone is slinging a rock of given mass around his head. Knowing the length of the sling and rotation rate find tangetial velocity of mass, centripital acceleration of rock, and tension in rope.
Tangential velocity: There is a very simple relationship between tangential velocity and angular velocity, you should find this in the beginning of the rotation section in your book, or easily online.
Centripetal acceleration: Centripetal acceleration for uniform circular motion is

$$a = \frac{v_{tan}^2}{r}$$
Tension: Tension is a measure of the force acting within a rope, use the above definition for centripetal acceleration, and Newton's second law.
#3. A wheel requires a given number of radians of rotation to accelerate from rest to a given angular rotation rate (in rad/sec). Find angular rate of acceleration, time to accelerate to given rotation rate, rotation rate after x seconds.

Very similar to #1
#4. A horizontal beam is attached to a frictionless hinge on a wall. Beam weight is given. A weight is placed on the beam at a given location. A VERTICAL cable supports the beam at the outer end. Find
tension in cable
x-component of force exerted on the beam by the wall
y-component of force exerted on the beam by the wall

(that VERTICAL cable is getting me)

Draw a force diagram of the system. What are the forces in the vertical direction? Hint: Gravity is one. You know the beam isn't moving, so you need to balance the gravitational force, what is doing that?

#5. A solid disc has a frictiionless axle running through its center, allowing it to rotate about this axis. Radius is given. Find tangetial force required to accelerate the disc from rest to a given rotation rate in a given number of seconds.
This is similar to #1 and #3 except you'll need to figure out a few more things than normally. Mostly rotational equations in conjunction with Newton's 2nd Law.
These are the main problems i am having. Sorry if these seem somewhat easy to some people, but i do not even know where to start on some of them. Thanks to anyone who helps.

Everyone learns sometime right? No ones born knowing physics.

Ok i believe i am understanding some of this a bit better. My progress so far:

epohxe said:
#1. Given a rotation rate in rad/sec and an accelleration rate in rad/sec^2, find:
a. Rotation rate after a given time in seconds
b. Angular displacement in radians during that time.

deltaTHETA = Wit + 1/2at^2 - angular displacement
w = Wi + at - rotation rate

(sorry i do not know how to insert nice looking formulas)

epohxe said:
#2. Someone is slinging a rock of given mass around his head. Knowing the length of the sling and rotation rate find tangetial velocity of mass, centripital acceleration of rock, and tension in rope.

Vt = rw - tangetiel velocity
Using above V - alpha = V^2tan/r - centripital acceleration
<still working on tension, not sure>

epohxe said:
#3. A wheel requires a given number of radians of rotation to accelerate from rest to a given angular rotation rate (in rad/sec). Find angular rate of acceleration, time to accelerate to given rotation rate, rotation rate after x seconds.

alpha = W/t - rate of acceleration
w = Wi + alpha t - Some rearranging to get t?
delta THETA = Wi t + 1/2 alpha t^2 - rotation rate after x seconds

epohxe said:
#5. A solid disc has a frictiionless axle running through its center, allowing it to rotate about this axis. Radius is given. Find tangetial force required to accelerate the disc from rest to a given rotation rate in a given number of seconds.

For this one, wouldn't you just have to find alpha = deltaW/deltaT and then use a = r alpha?

learn latex it aint that hard look for the link in the sticky in the general physics forums
for the first one you are correct
$$\omega_{2} = \omega_{1} + \alpha t$$
$$\Delta \theta = \omega_{1} t + \frac{1}{2} \alpha t^2$$

for the second one

tangential velocity is simply the angular velocity (vector) times the radial (radius) vector. That is tangential velcoity $v = r \omega$

Centripetal Acceleration is simply $$\frac{mv^2}{r}$$ no tan or sin or whatever if there is no angle with respect to the axis of rotation. here the angle is 90 so you don't have to worry about that

As for the tension in the string. Since this is a perfectly horizontal circle draw a sideways view of the block going into the page - what forces act on it?? Centripetal and gravitational. The String must balance these forces to keep itself horizontal. Draw a diagram and show us what you got.

For hte third one
everything is fine except for the last one wher they ask you the rotation RATE not DISPLACEMENT after x seconds. What is the Rotation Rate?

For hte Fifth one
certainly $$\alpha = \frac{\omega}{t}$$
taht s the acceleration required to get it to move. Now to move anything circular you need TORQUE whic his calculated using $$\tau = I \alpha$$
where I is the moment of inertia for the object in question.
now furtermore torque $$\tau = R F \sin \theta$$
where R is the radius of the tangeital force F, and the theta is the angle the force makes with the radial vector. Since it is TANGENTIAL theta is 90 so $$\tau = RF$$

Last edited:
Centripetal Acceleration is simply $$\frac{mv^2}{r}$$ no tan or sin or whatever if there is no angle with respect to the axis of rotation. here the angle is 90 so

This is a force, and "vtan" means $$v_{tan(gential)}$$

alpha = W/t - rate of acceleration
w = Wi + alpha t - Some rearranging to get t?
delta THETA = Wi t + 1/2 alpha t^2 - rotation rate after x seconds

This is correct ,but make sure you know the difference between average angular acceleration/angular velocity and final angular acceleration/angular velocity. These equations are both correct though, the last one is not necessary. It's asking you for a rate of rotation.. a velocity. One of the above already takes care of this.

#5. A solid disc has a frictiionless axle running through its center, allowing it to rotate about this axis. Radius is given. Find tangetial force required to accelerate the disc from rest to a given rotation rate in a given number of seconds.

Hints:
Using radius, centripetal acceleration, and the relationship btwn tangential and angular acceleration you can figure this one out. It wants you to accelerate a disk from rest to a certain speed (you know how to do this) by accelerating it tangent to the radius. How does linear acceleration and angular acceleration relate? that's pretty much all you need.

Ok, with your help i feel confident about these problems. I have just figured out the horizontal beam one:

epohxe said:
#4. A horizontal beam is attached to a frictionless hinge on a wall. Beam weight is given. A weight is placed on the beam at a given location. A VERTICAL cable supports the beam at the outer end. Find

tension in cable
x-component of force exerted on the beam by the wall
y-component of force exerted on the beam by the wall

Three equations, leaving sin theta in assuming there is an angle in the cable and not vertical:

1. $$R_(x) - T cos \theta = 0$$
2. $$R_(y) + T sin \theta - (\mbox{weight of objectt}) - 300 N = 0$$
3. $$(T sin \theta)(\mbox{length of boardt}) - (300\ N)(\mbox{length to center of gravity}) - (\mbox{weight of object})(\mbox{distance to object}) = 0$$

Solve for T on the last one and plug into the first two.

## 1. What is the difference between angular velocity and angular acceleration?

Angular velocity refers to the rate at which an object rotates around a fixed axis. It is measured in radians per second. On the other hand, angular acceleration is the rate of change of angular velocity. It is measured in radians per second squared.

## 2. How does the radius of rotation affect the angular velocity?

The radius of rotation is directly proportional to the angular velocity. This means that as the radius increases, the angular velocity also increases, and vice versa. This relationship is known as the law of conservation of angular momentum.

## 3. What is the difference between centripetal force and centrifugal force?

Centripetal force is the force that keeps an object moving in a circular motion. It acts towards the center of the circle and is responsible for changing the direction of an object's velocity. On the other hand, centrifugal force is a fictitious force that appears to act outwards on an object in circular motion. It is a reaction force to the centripetal force and is not a real force.

## 4. How does the moment of inertia affect rotational motion?

The moment of inertia is a measure of an object's resistance to changes in its rotational motion. The higher the moment of inertia, the more force is required to change an object's angular velocity. This means that objects with a higher moment of inertia will have a slower rotational motion compared to objects with a lower moment of inertia.

## 5. Can you explain the concept of torque?

Torque is a measure of the twisting force that causes an object to rotate around an axis. It is calculated by multiplying the force applied by the distance from the axis of rotation. The direction of the torque is perpendicular to both the force and the distance. Torque is also responsible for changing an object's angular momentum.

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