1) Consider a bowling ball of 9.50 kg, a moment of inertia of 2.80E-02 kg·m², and a radius of 0.150 m. If it rolls down the lane without slipping at a linear speed of 7.50 m/s, what is its total kinetic energy?2) A 2.5 kg mass is moving in a straight line at 12.5 m/s towards the edge of a disk with a diameter of 1.5 m.  The angular momentum of the mass, in kg m2/s, is most nearly?3)A child sits on a carousel at a distance of 8.50 m from the center and rotates through an arc length of 6.50 m. What is the angular displacement of the child?3) You are attempting to lift a 350 kg sofa to your third-floor apartment building using a pulley system that has a mechanical advantage of 12.  Which force must be exerted by you to lift the sofa? 4) An automobile tire with a radius of 0.30 m accelerates from rest at a constant 2.0 rad/s².  What is the tangential component of acceleration for a point on the outer edge of the tire?5)A bucket filled with water has a mass of 23.0 kg and is attached to a rope that is wound around a cylinder with a radius of 0.15 m at the top of a well. What torque does the load produce on the cylinder?

Question
Asked Oct 11, 2019
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1) Consider a bowling ball of 9.50 kg, a moment of inertia of 2.80E-02 kg·m², and a radius of 0.150 m. If it rolls down the lane without slipping at a linear speed of 7.50 m/s, what is its total kinetic energy?

2) A 2.5 kg mass is moving in a straight line at 12.5 m/s towards the edge of a disk with a diameter of 1.5 m.  The angular momentum of the mass, in kg m2/s, is most nearly?

3)A child sits on a carousel at a distance of 8.50 m from the center and rotates through an arc length of 6.50 m. What is the angular displacement of the child?

3) You are attempting to lift a 350 kg sofa to your third-floor apartment building using a pulley system that has a mechanical advantage of 12.  Which force must be exerted by you to lift the sofa? 

4) An automobile tire with a radius of 0.30 m accelerates from rest at a constant 2.0 rad/s².  What is the tangential component of acceleration for a point on the outer edge of the tire?

5)A bucket filled with water has a mass of 23.0 kg and is attached to a rope that is wound around a cylinder with a radius of 0.15 m at the top of a well. What torque does the load produce on the cylinder?

 

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Expert Answer

Step 1

The condition for pure rolling is

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= »R cm

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Step 2

 

Here vcm is the linear velocity of the ball of the velocity of the center of mass of the ball, ω is the angular velocity of the ball, R is the radius of the ball,

The angular speed of the ball can be calculated from the above relation.

Substitute 7.5 m/s for vcm, 0.150 m for R an solve for ω,

 

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7.5m/s (0.150m) 7.5m/s 0.150m 50rad/s o

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Step 3

The kinetic energy of the rolling ball without slipping is defined as the sum of its rotati...

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1 K.E -Ia mv, 2 2 ст 2

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Rotational Mechanics

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