11.1 Rolling Motion

The no-slip condition linking center-of-mass speed to spin rate, the static friction it demands, and energy methods for objects on inclines.

University Physics Volume 1, 11.1 Rolling Motion

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12 exercises

11.1 Exercise 1

A hollow cylinder is on an incline at an angle of $60 ° .$ The coefficient of static friction on the surface is $\mu_{s} = 0.6$ . (a) Does the cylinder roll without slipping? (b) Will a solid cylinder roll without slipping?

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11.1 Exercise 2

Can a round object released from rest at the top of a frictionless incline undergo rolling motion?

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11.1 Exercise 4

A wheel is released from the top on an incline. Is the wheel most likely to slip if the incline is steep or gently sloped?

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11.1 Exercise 6

A hollow sphere and a hollow cylinder of the same radius and mass roll up an incline without slipping and have the same initial center of mass velocity. Which object reaches a greater height before stopping?

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11.1 Exercise 7

What is the angular velocity of a 75.0-cm-diameter tire on an automobile traveling at 90.0 km/h?

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11.1 Exercise 9

If the boy on the bicycle in the preceding problem accelerates from rest to a speed of 10.0 m/s in 10.0 s, what is the angular acceleration of the tires?

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11.1 Exercise 11

A marble rolls down an incline at $30 °$ from rest. (a) What is its acceleration? (b) How far does it go in 3.0 s?

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11.1 Exercise 13

A rigid body with a cylindrical cross-section is released from the top of a $30 °$ incline. It rolls 10.0 m to the bottom in 2.60 s. Find the moment of inertia of the body in terms of its mass m and radius r.

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11.1 Exercise 15

A solid cylinder of radius 10.0 cm rolls down an incline with slipping. The angle of the incline is $30 ° .$ The coefficient of kinetic friction on the surface is 0.400. What is the angular acceleration of the solid cylinder? What is the linear acceleration?

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11.1 Exercise 17

A 40.0-kg solid cylinder is rolling across a horizontal surface at a speed of 6.0 m/s. How much work is required to stop it?

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11.1 Exercise 19

A solid cylinder rolls up an incline at an angle of $20 ° .$ If it starts at the bottom with a speed of 10 m/s, how far up the incline does it travel?

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11.1 Exercise 21

A hollow cylinder that is rolling without slipping is given an initial velocity and rolls up an incline to a vertical height of 1.0 m. If a hollow sphere of the same mass and radius is given the same initial velocity, how high vertically does it roll up the incline?

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