Rotational Kinematics
& Tangential vs Centripetal
& Tangential vs Centripetal
Torque
Moment of Inertia
Vocabulary
100
Two ladybugs are on a spinning disk. One lady bug is closer to the center of the disk, and the other is closer to the edge of the disk. How do their angular velocities compare?
They are the same.
BONUS OPPORTUNITY: How do their linear velocities compare?
100
Why does increasing the length of a wrench increases the torque?
The distance from the axis of rotation increases.
100
What are the units for I?
kg m^2
100
The rotational analogue of FORCE
Torque
200
To convert from tangential kinematic quantities to angular kinematic quantities, what should you do?
Divide by the radius
200
A uniform 4 m beam of mass 10 kg is supported horizontally at one end. Find the torque due to gravity about the support.
196.2 Nm
200
A spinning disk is slowing down due to friction. What happens to its rotational inertia?
Stays the same
200
The tendency of an object to resist a change to its rotational state.
Moment of Inertia
300
A wheel starts from rest and accelerates at 2 rad/s2 for 5 seconds. Find its angular displacement.
25 rad
300
A disk of mass 10 kg (I=1/2MR2) is subjected to a 15 N force at a radius of 0.4 m. Find the angular acceleration.
7.5 rad/s2
300
In a solar system model of three rocky planets, there are only 3 objects (Mercury, Venus, and Earth). Mercury has a mass of 3 kg, Venus has a mass of 8 kg, and Earth has a mass of 9 kg. If their distances away from the sun are, respectively, 1 m, 3 m, and 8 m, what is the total moment of inertia for the system?
651 kgm2
300
The name for the acceleration that pulls towards the center of curvature for a curved path.
(Hint: for an object with constant speed, this acceleration would be directed towards the center of a circle)
What is Centripetal Acceleration
Bonus: Give a formula for centripetal acceleration in terms of angular velocity, and another in terms of linear velocity.
400
The angular position of a rotating object, given by the function theta=2t^2-5t+4 , where t is time in seconds and theta is the angular position in radians. The objects' angular velocity at t=2s is _______________.
What is 3 rad/s
400
A bar of length 1m sits on a pivot located at its center. At the instant shown in the figure, the bar is horizontal and two forces F1 and F2 are exerted on its ends as indicated. The NET Torque on the bar is ______________.
10 Nm
400
Determine the moment of inertia for each system. P represents the pivot points for each system.
1) 4MD^2
2) 8MD^2
3) 8MD^2
400
The name for the component of acceleration, caused by a non-zero net torque, that is NOT directed towards the center of the curvature.
What is TANGENTIAL ACCELERATION
500
A coin sits near the edge of a platform with Radius R . The platform is initially at rest when it begins to rotate with a constant angular acceleration alpha such that its angular velocity omega increases linearly with time. The magnitude and direction of the coin are __________ .
What is equal to
sqrt((R omega^2)^2 + (R alpha)^2)
500
A board can pivot on a hinge as shown in the figure. Rank the forces by the magnitudes of the torques they produce.
Torque from 2Fo is greatest.
The other torques are lesser but equal to one another.
500
An initially hollow cube is crushed with enough force to make it into a solid cube. For a rotation axis that runs through the center of the cube and the centers of two opposite faces of the cube, how does the moment of inertia change as the cube is crushed?
It decreases.
500
What is the state in which a system has total net force of zero and total net torque of zero?
Spell the word correctly, and give an example
What is EQUILIBRIUM
and
(answers may vary) - my example: a ladder at rest leaning on a building