Group 5- Rotation

If you go around a circle 8 times what is your angular displacement?

16pi radians

How many radians are in one circle?

2pi radians

You have a seesaw with a 20 N child sitting 8 m to the left of the center pivot. Where should a 40 N child sit to perfectly balance it out?

4 m to the right of the pivot

If you go around a circle 9 times in 3 seconds what is your angular velocity?

6pi radians/sec

What is Newton's 1st Law for rotating objects?

a object not rotating at a constant angular velocity, along the same x axis, unless acted upon by a net external torque

Sometimes a torque producing force F is not acting perpendicular to the lever arm but at some angle theta less than 90 degrees. What is the magnitude of the perpendicular component of this force?

Fsin(theta)

What is the equation for the kinetic energy an object has because it is rotating?

Krot=1/2 w^2

What is the symbol for angular momentum?

L

What is the equation for the angular momentum of an object?

L=lw

What are the units of torque?

Nm

What is Newton's 2nd Law for rotational motion?

Tnet-la Net torque=rotational mass x angular acceleration

What is a torque?

a twisting push or pull

What is the symbol for angular acceleration?

alpha

For every LINEAR motion kinematics equations there is a what?

an equivalent rotational motion kinematics equation

When figure skaters start a slow spin, and then pull in their arms and legs they "spin up". Explain.

at the beginning of the spin they have their arms and legs spread out, far from the axis of ration. therefore they have a large l value. when they pull in their arms their l value goes down. however, they must still conserve angular momentum which is lw. so if l gets smaller, then w must get larger, to preserve the original lw value

What are the two basic types of torques?

clockwise and counter-clockwise

How do you convert linear displacements, velocities, and accelerations into their angular counterparts?

divide by the radius of the circle

What is the Law of Conservation of Momentum- MODERN physics style?

in a closed system, the total angular momentum of an object or system before an event must be the same as the total angular momentum after an event

What can clockwise torque do?

it can cancel out counter-clockwise torque

What does it mean if you have an angular acceleration of 4 rad/sec^2?

it means that your angular velocity is changing 4 radians/sec every second

What two things determine the rotational mass of an object?

it's regular mass, and the distribution of that mass relative to the axis of rotation

What is another name for rotational mass?

moment of inertia

How can you increase the rotational mass of an object without changing its inertial mass?

move the mass farther away from the axis of rotation

How do you convert angular displacements, velocities and accelerations into linear counterparts?

multiply by the radius of the circle

Assuming that the force is ACTING PERPENDICULAR to the lever arm, how do you calculate the magnitude of the torque acting on the object?

multiply the force by the lever arm distance

When a spinning object collapses and speeds up is angular kinetic energy conserved? Explain.

no. work must be done on the object to pull the mass towards the center, which increases the angular KE

What is the symbol for angular velocity?

omega

If you have gone through 1 radian of angle then how much linear distance have you travelled?

one radius of distance

How many radians are in half a circle?

pi radians

How many radians are in a quarter circle?

pi/2 radians

How do you create a torque on a body floating in space?

place a force on it that does NOT go through the center of gravity

How do you create a torque on a door or a seesaw?

place a force on it that does NOT go through the hinge

To produce a torque a force must NOT be doing what?

pointing right at the hinge or center of gravity

Does an object only have on rotational mass? Explain.

since an object can be spun around many different axes it will have a different rotational mass for each different kind of spin

What can you do with a net torque/angular position graph?

take the area between the line and the x axis to get the total change in angular KE

What can you do with a net torque/time graph?

take the area between the line and the x axis to get the total change in angular momentum

What can you do with an angular velocity/time graph?

take the slope to find the angular acceleration OR take the area between the line and the x axis to get angular displacement

What can you do with an angular position/time graph?

take the slope to find the angular velocity

What is the symbol for torque?

tau

You have a ball and a square block, of equal mass, sitting at the top of a ramp. The ball rolls down the ramp without slipping, the square block slides down the ramp with no friction. If they are both released at the same moment, which will reach the bottom first?

the block will arrive at the bottom first. both objects have the same potential energy at the top of the ramp. the block gets to convert ALL of this energy into just LINEAR KE for moving down the ramp quickly. the rolling ball has to convert some of its potential energy into ROTATIONAL KE leaving less available or the LINEAR KE it needs to move down the ramp

What do we call the distance between a force trying to produce a force trying to produce a torque and the hinge or center of gravity of the object?

the lever arm

The net torque on an object, multiplied by the time over which that torque acted, is called what? What other number is this number equal to?

the net angular impulse. it is exactly equal to the change in angular momentum of the object

The net torque on an object, multiplied by the angular displacement over which that torque acted, is called what? What other number is this number equal to?

the net angular work. it is exactly equal to the change in angular kinetic energy of the object

You have two round objects of equal mass and equal radius. One is a hollow steel ring, the other is a solid wooden disc. You release them from the top of a ramp and they start rolling down the ramp at the same moment. Which one will reach the bottom of the ramp first? Explain.

the solid wooden disk will get to the bottom first. since more of its mass is closer to the axis of the rotation, its rotational mass is smaller, and therefore it is easier to angularly accelerate

What are two simple statements of the Law of Conservation of Angular Momentum?

the total amount of spin in the universe must remain constant, or, whenever one object loses spin another must gain it

What is the symbol for angular displacement?

theta

What are 3 ways of saying Newton's 3rd Law for rotational motion?

to get a torque you must give a torque, torques always come in pairs, for every action there is an equal and opposite reaction

What is a net torque?

when many torques are acting simultaneously on an object it is the final torques that is left after all the clockwise and counterclockwise torques have either added together or cancelled out