Angular Velocity

A rope swing is 3 meters long and is rotating at 90 deg/s. what's the centripetal acceleration?

• 7.4 m/s/s

• 2700 m/s/s

• 270 m/s/s

• 4.7 m/s/s

• I'm confused

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NGSS.HS-PS2-1

A quarterback's arm is 0.8 meters long and rotating at 4 rad/s at release. How fast is the ball moving?

• 5 m/s

• 3.2 m/s

• 20 m/s

• 183 m/s

• None of the above

If I wanted to throw a baseball 44.7 m/s (100mph) with an arm that is 0.7 m long, how fast would I have to rotate?

• 64 deg/s

• 64 m/s

• 64 rad/s

• 31 deg/s

• 31 rad/s

A merry-go-round disk with a rotational inertia of I_d about its center spins around its center axle with an initial angular velocity of ω₀. A child is standing near the edge of the merry-go-round, as shown in Figure 1. The child’s rotational inertia about the center of the disk when near the edge is I₀. As the merry-go-round spins, the child moves closer to the center, as shown in Figure 2, until the disk rotates with an angular velocity of ω₁. Which of the following equations could a student use to determine the rotational inertia I_s of the child-merry-go-round system about the center axle immediately after the child has moved to the location shown in Figure 2? Justify your selection.

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7.4 Conservation of Angular Momentum

An isolated spherical star of radius R₀ rotates about an axis that passes through its center with an angular velocity of ω₀. Gravitational forces within the star cause the star’s radius to collapse and decrease to a value r₀ < R₀, but the mass of the star remains constant. A graph of the star’s angular velocity as a function of time as it collapses is shown. Which of the following predictions is correct about the angular momentum L of the star immediately after the collapse?

• L will be greater after the collapse

• L will be less after the collapse

• L will remain the same before and after the collapse

• L will be the same after the collapse, but will change direction

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7.4 Conservation of Angular Momentum

A point on the edge of a disk rotates around the center of the disk with an initial angular velocity of 3rad/s3rad/s clockwise. The graph shows the point’s angular acceleration as a function of time. The positive direction is considered to be counterclockwise. All frictional forces are considered to be negligible.

How can the graph be used to determine the angular speed of the disk after 2s2s? Justify your selection.

• Determine the area bound by the line and the horizontal axis from 0s to 2s , because this area represents the final angular velocity of the point on disk.

• Determine the area bound by the line and the horizontal axis from 0s to 2s , because this area represents the change in the angular velocity of the point on disk.

• Determine the vertical-axis intercept, because this value represents the final angular velocity of the point on disk.

• Determine the slope of the line, because this value represents the change in the angular velocity of the point on disk.

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7.1 Rotational Kinematics

A point on a disk rotates around the center axle of the disk. The table shows the angular speed of the point as a function of time. Which of the following graphs could represent the angular position of the point as a function of time?

• 
• 
• 
• 

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7.1 Rotational Kinematics

• An equation is not necessary, because the point on the edge of the disk will have the same angular displacement regardless of its initial angular velocity.

• The angular displacement cannot be determined because an equation that includes a term for time must be used.

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7.1 Rotational Kinematics

A wheel is rotating at 10 rad/s. What is its angular velocity in degrees per second?

• 360 deg/s

• 180 deg/s

• 600 deg/s

• 10 deg/s

If a disc spins at 5 revolutions per second, what is its angular velocity in radians per second?

• 10 rad/s

• 15.7 rad/s

• 31.4 rad/s

• 5 rad/s