Essential University Physics (3rd Edition)
3rd Edition
ISBN: 9780134202709
Author: Richard Wolfson
Publisher: PEARSON
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Chapter 11, Problem 59P
A solid ball of mass M and radius R is spinning with
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Solid spheres have a rotational inertia about an axis through their center of mass given by I = 2/5 M R2, where M is the mass of the sphere and R is the radius of the sphere. Consider a particular sphere of radius 1.2 m made out of a material of density 300 kg/m3. Using the parallel axis theorem, calculate the rotational inertia of the sphere about a parallel axis shifted 0.33 m away from the center.
(Please answer to the fourth decimal place - i.e 14.3225)
a solid cylinder of radius 10 cm and mass 12 kg starts from rest and rolls without slipping a distance L = 6.0 m down a roof that is inclined at angle u = 30 . (a)What is the angular speed of the cylinder about its center as it leaves the roof? (b) The roof’s edge is at height H = 5.0 m. How far horizontally from the roof’s edge does the cylinder hit the level ground?
Consider a wheel (solid disk) of radius 0.992 m, mass 19 kg and moment of inertia 1/2 M R2. The wheel rolls without slipping in a straight line in an uphill direction 26 ◦ above the horizontal. The wheel starts at angular speed 22.7823 rad/s but the rotation slows down as the wheel rolls uphill, and eventually the wheel comes to a stop and rolls back downhill.How far does the wheel roll in the uphill direction before it stops? The acceleration of gravity is 9.8 m/s^2.Answer in units of m.
Chapter 11 Solutions
Essential University Physics (3rd Edition)
Ch. 11.1 - Youre standing on the sidewalk watching a car go...Ch. 11.2 - The figure shows four pairs of force and radius...Ch. 11.3 - The figure shows three particles with the same...Ch. 11.4 - You step onto an initially nonrotating turntable...Ch. 11.5 - You push horizontally at right angles to the shaft...Ch. 11 - Does Earths angular velocity vector point north or...Ch. 11 - Figure 11.12 shows four forces acting on a body....Ch. 11 - You stand with your right arm extended...Ch. 11 - Although it contains no parentheses, the...Ch. 11 - Whats the angle between two vectors if their dot...
Ch. 11 - Why does a tetherball move faster as it winds up...Ch. 11 - Why do helicopters have two rotors?Ch. 11 - A group of polar bears is standing around the edge...Ch. 11 - Tornadoes in the northern hemisphere rotate...Ch. 11 - Does a particle moving at constant speed in a...Ch. 11 - When you turn on a high-speed power tool such as a...Ch. 11 - Why is it easier to balance a basketball on your...Ch. 11 - A bug, initially at rest on a stationary,...Ch. 11 - If you increase the rotation rate of a precessing...Ch. 11 - A car is headed north at 70 km/h. Give the...Ch. 11 - If the car of Exercise 15 makes a 90 left turn...Ch. 11 - A wheel is spinning at 45 rpm with its axis...Ch. 11 - A wheel is spinning about a horizontal axis with...Ch. 11 - A 12-N force is applied at the point x = 3 m, y =...Ch. 11 - A force F=1.3i+2.7jN is applied at the point x =...Ch. 11 - When you hold your arm outstretched, its supported...Ch. 11 - Express the units of angular momentum (a) using...Ch. 11 - In the Olympic hammer throw, a contestant whirls a...Ch. 11 - A gymnast of rotational inertia 62 kg m2 is...Ch. 11 - A 640-g hoop 90 cm in diameter is rotating at 170...Ch. 11 - A 7.4-cm-diameter baseball has mass 145 g and is...Ch. 11 - A potters wheel with rotational inertia 6.40 kg ...Ch. 11 - A 3.0-m-diametcr merry-go-round with rotational...Ch. 11 - A uniform, spherical cloud of interstellar gas has...Ch. 11 - A skater has rotational inertia 4.2 kg m2 with...Ch. 11 - You slip a wrench over a bolt. Taking the origin...Ch. 11 - Vector A points 30 counterclockwise from the...Ch. 11 - A baseball player extends his arm straight up to...Ch. 11 - Prob. 34PCh. 11 - A weightlifters barbell consists of two 25-kg...Ch. 11 - Prob. 36PCh. 11 - Two identical 1800-kg cars are traveling in...Ch. 11 - The dot product of two vectors is half the...Ch. 11 - Biomechanical engineers have developed...Ch. 11 - Figure 11.15 shows the dimensions of a 880-g...Ch. 11 - As an automotive engineer, youre charged with...Ch. 11 - A turntable of radius 25 cm and rotational inertia...Ch. 11 - A 17-kg dog is standing on the edge of a...Ch. 11 - A physics student is standing on an initially...Ch. 11 - Youre choreographing your schools annual ice show....Ch. 11 - Find the angle between two vectors whose dot...Ch. 11 - A circular bird feeder 19 cm in radius has...Ch. 11 - A force F applied at the point x = 2.0 m, y = 0 m...Ch. 11 - Prob. 49PCh. 11 - Prob. 50PCh. 11 - Jumbo is back! Jumbo is the 4.8-Mg elephant from...Ch. 11 - An anemometer for measuring wind speeds consists...Ch. 11 - A turntable has rotational inertia I and is...Ch. 11 - A uniform, solid, spherical asteroid with mass 1.2...Ch. 11 - About 99.9% of the solar systems total mass lies...Ch. 11 - Youre a civil engineer for an advanced...Ch. 11 - In Fig. 11.18, the lower disk, of mass 440 g and...Ch. 11 - A massless spring with constant k is mounted on a...Ch. 11 - A solid ball of mass M and radius R is spinning...Ch. 11 - A time-dependent torque given by = a + b sin ct...Ch. 11 - Consider a rapidly spinning gyroscope whose axis...Ch. 11 - When a star like our Sun exhausts its fuel,...Ch. 11 - Pulsarsthe rapidly rotating neutron stars...Ch. 11 - Prob. 64PCh. 11 - Figure 11.22 shows a demonstration gyroscope,...Ch. 11 - Figure 11.22 shows a demonstration gyroscope,...Ch. 11 - Figure 11.22 shows a demonstration gyroscope,...Ch. 11 - Figure 11.22 shows a demonstration gyroscope,...
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- A disk 8.00 cm in radius rotates at a constant rate of 1200 rev/min about its central axis. Determine (a) its angular speed in radians per second, (b) the tangential speed at a point 3.00 cm from its center, (c) the radial acceleration of a point on the rim, and (d) the total distance a point on the rim moves in 2.00 s.arrow_forwardThe propeller of an aircraft accelerates from rest with an angular acceleration = 4t + 6, where is in rad/s2 and t isin seconds. What is the angle in radians through which thepropeller rotates from t = 1.00 s to t = 6.00 s?arrow_forwardIf the angular acceleration of a rigid body is zero, what is the functional form of the angular velocity?arrow_forward
- A hollow sphere of radius 0.160 m, with rotational inertia I = 0.0778 kg·m2 about a line through its center of mass, rolls without slipping up a surface inclined at 40.6° to the horizontal. At a certain initial position, the sphere's total kinetic energy is 55.0 J. (a) How much of this initial kinetic energy is rotational? (b) What is the speed of the center of mass of the sphere at the initial position? When the sphere has moved 0.910 m up the incline from its initial position, what are (c) its total kinetic energy and (d) the speed of its center of mass?arrow_forward9.8 ● A wheel is rotating about an axis that is in the z-direction. The angular velocity w is -6.00 rad/s at t = 0, increases lin- early with time, and is +8.00 rad/s at t = 7.00 s. We have taken counterclockwise rotation to be positive. (a) Is the angular acceleration during this time interval positive or negative? (b) During what time interval is the speed of the wheel increasing? Decreasing? (c) What is the angular displacement of the wheel at t = 7.00 s?arrow_forwardA wheel of radius 0.328 m, which is moving initially at 48.4 m/s, rolls to a stop in 285 m. Calculate the magnitudes of (a) its linear acceleration and (b) its angular acceleration. (c) The wheel's rotational inertia is 1.48 kg · m2 about its central axis. Calculate the magnitude of the torque about the central axis due to friction on the wheel. (a) Number i Units (b) Number i Units (c) Number i Units > >arrow_forward
- 9.15 A high-speed flywheel in a motor is spinning at 500 rpm when a power failure suddenly occurs. The flywheel has mass 40.0 kg and diameter 75.0 cm. The power is off for 30.0 s, and during this time the flywheel slows due to friction in its axle bearings. During the time the power is off, the flywheel makes 200 complete revolu- tions. (a) At what rate is the flywheel spinning when the power comes back on? (b) How long after the beginning of the power failure would it have taken the flywheel to stop if the power had not come back on, and how many revolutions would the wheel have made during this time? ●●arrow_forwardA wheel of radius 0.250 m, moving initially at 43.0 m/s, rolls to a stop in 225 m. Calculate the magnitudes of its (a) linear acceleration and (b) angular acceleration. (c) Its rotational inertia is 0.155 kg m2 about its central axis. Find the magnitude of the torque about the central axis due to friction on the wheel.arrow_forward9.45 .. Energy is to be stored in a 70.0-kg flywheel in the shape of a uniform solid disk with radius R = 1.20 m. To prevent struc- tural failure of the flywheel, the maximum allowed radial accelera- tion of a point on its rim is 3500 m/s². What is the maximum kinetic energy that can be stored in the flywheel?arrow_forward
- In the figure, a solid cylinder of radius 24.0 cm and mass 17.0 kg starts from rest and rolls without slipping a distance L = 5.70 m down a roof that is inclined at angle θ = 40°. (a) What is the angular speed of the cylinder about its center as it leaves the roof? (b) The roof's edge is at height H = 6.70 m. How far horizontally from the roof's edge does the cylinder hit the level ground?arrow_forwardA turntable has rotational inertia I and is rotating with angular speed w about a frictionless vertical axis. A wad of clay with mass m is tossed onto the turntable and sticks a distance d from the rotation axis. The clay hits horizontally with its velocity at right angles to the turntable's radius, and in the same direction as the turntable's rotation (Fig. 11.17). Find expressions for v that will result in (a) the turntable's angular speed dropping to half its initial value, (b) no change in the turntable's angular speed, and (c) the angular speed doubling.arrow_forwardA solid cylinder of mass 2.7 kg and radius 0.48 m starts from rest at the top of a ramp, inclined 28°, and rolls to the bottom without slipping(For a cylinder I =; 0.5MR^2) The upper end of the ramp is 2.3 m higher than the lower end. Find the linear velocity of the cylinder when it reaches the bottom of the ramp? (g = 9.8 m/s^2)arrow_forward
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