# Rotational Motion (Grades 11-12)

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## Rotational Motion

1.

In the diagram below, what force is required to keep an object of mass [math]m[/math] from slipping off the disk?

- [math]mg[/math]
- [math](mv^2)/r[/math]
- [math](mv^2)/(2g)[/math]
- [math](2pimg)/v^2[/math]

2.

In the figure below, the force exerted by the person on the mass is called force.

- Centrifugal
- Centripetal
- Gravitational
- Ellastic

3.

If a particle moves in a plane so that its position is described by the functions

[math]x=Acosomegat[/math] and [math]y=Asinomegat[/math], the particle is

[math]x=Acosomegat[/math] and [math]y=Asinomegat[/math], the particle is

- moving with constant speed along a circle.
- moving with varying speed along a circle.
- moving with constant acceleration along a straight line.
- moving along a parabola.
- oscillating back and forth along a straight line.

4.

The rate at which a rotating object spins, its angular velocity, can be expressed in all of the following ways except:

- degrees/sec.
- rotations/sec.
- rad/sec.
- rpm.
- revolutions/sec.

5.

A wind turbine, with 4m long blades, turns at a rotor speed of 2.9rad/3s. What is the linear velocity of the tip of the blade?

Given: [math]v=omegar[/math]

Given: [math]v=omegar[/math]

6.

Jupiter has the fastest rotation of all the planets in the Solar System, completing one rotation on its axis every 9.9 hours. The rapid rotation causes the planetâ€™s equator to bulge out. Instead of being a perfect sphere, Jupiter looks more like a squashed ball. What is its angular velocity in radians per second?

Given: [math]2pi" rad"=360deg[/math]

[math]omega="angular velocity in rad/s"[/math]

[math]DeltaTheta="change in angle in radians"[/math]

[math]Deltat="change in time in seconds"[/math]

[math]omega=(DeltaTheta)/(Deltat)[/math]

Given: [math]2pi" rad"=360deg[/math]

[math]omega="angular velocity in rad/s"[/math]

[math]DeltaTheta="change in angle in radians"[/math]

[math]Deltat="change in time in seconds"[/math]

[math]omega=(DeltaTheta)/(Deltat)[/math]

7.

In the diagram below, calculate the minimum value of friction coefficient [math]mu[/math] between the person's feet and the floor required to prevent the person from slipping. Express your answer in terms of the person's mass [math]M[/math], any quantities shown on the diagram, and fundamental constants. Assume the ball of mass [math]m[/math] is being swung in the horizontal plane.

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