Rotational Kinetic Energy

A child kicks a ball which rolls across a field with a velocity of 5 m/s. You may assume the ball doesn’t slip, and treat it as a hollow sphere of mass 0.43 kg and radius 0.11 meter.

What is the ball’s rotational velocity?

• 45.5 rad/s

• 0.047 rad/s

• 413 rad/s

• 0.0605 rad/s

A child kicks a ball which rolls across a field with a velocity of 5 m/s. You may assume the ball doesn’t slip, and treat it as a hollow sphere of mass 0.43 kg and radius 0.11 meter.

What is the ball’s translational (linear) kinetic energy in joules?

Tags

NGSS.HS-PS3-1

A child kicks a ball which rolls across a field with a velocity of 5 m/s. You may assume the ball doesn’t slip, and treat it as a hollow sphere of mass 0.43 kg and radius 0.11 meter.

What is the ball's total kinetic energy in joules?

• about 9 J

• about 5.5 J

• about 13 J

Tags

NGSS.HS-PS3-1

NGSS.HS-PS3-2

 $I=\frac{2}{5}mr^2$  

A bowling ball of mass M and radius R rolls without
slipping along a level surface at speed v. The maximum vertical height to which it can roll if it ascends an
incline is

•  $\frac{v^2}{5g}$  

•  $\frac{2v^2}{5g}$  

•  $\frac{v^2}{2g}$  

•  $\frac{7v^2}{10g}$  

•  $\frac{v^2}{g}$  

Tags

NGSS.HS-PS3-1

NGSS.HS-PS3-2

A sphere of mass M, radius r, and rotational inertia I is released from rest at the top of an inclined plane of height h.

If the plane is frictionless, what is the speed of the center of mass of the sphere at the bottom of the incline?

• $\sqrt{2gh}$

• $\frac{2Mgh}{I}$

• $\frac{2Mghr^2}{I}$

• $\sqrt{\frac{2Mghr^2}{I}}$

• $\sqrt{\frac{2Mghr^2}{I+Mr^2}}$

Tags

NGSS.HS-PS3-1

NGSS.HS-PS3-2

A sphere of mass M, radius r, and rotational inertia I is released from rest at the top of an inclined plane of height h.

If the plane is not frictionless, what is the speed of the center of mass of the sphere at the bottom of the incline?

• $\sqrt{2gh}$

• $\frac{2Mgh}{I}$

• $\frac{2Mghr^2}{I}$

• $\sqrt{\frac{2Mghr^2}{I}}$

• $\sqrt{\frac{2Mghr^2}{I+Mr^2}}$

Tags

NGSS.HS-PS2-1

NGSS.HS-PS3-1

Which equation defines kinetic energy?

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Tags

NGSS.HS-PS3-1

NGSS.HS-PS3-2

Which equation defines the relationship between linear velocity and angular velocity?

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Which equation defines rotational kinetic energy?

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Tags

NGSS.HS-PS3-2

A bowling ball has a mass of 7.00 kg, a moment of inertia of 2.80 × 10⁻² kg·m², and a radius of 0.100 m. If it rolls down the lane without slipping at an angular speed of 4.00 rad/s, what is its rotational kinetic energy?

• 0.280 J

• 0.448 J

• 0.224 J

• 11.2 J

Tags

NGSS.HS-PS3-1