Essential University Physics (3rd Edition)
3rd Edition
ISBN: 9780134202709
Author: Richard Wolfson
Publisher: PEARSON
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Chapter 11, Problem 5FTD
What’s the angle between two vectors if their dot product is equal to the magnitude of their cross product?
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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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- Show that when A+B=C then A2+B2+2ABcos , where is the angle between vectors A and B .arrow_forwardWhich of the following statements is true about the relationship between the dot product of two vectors and the product of the magnitudes of the vectors? (a) AB is larger than AB. (b) AB is smaller than AB. (c) AB could be larger or smaller than AB, depending on the angle between the vectors. (d) AB could be equal to AB.arrow_forwardWhat is the scaler product and the angle?arrow_forward
- The magnitude of dot and cross product of two vectors 6V3 ando respectively. Find the angle between the vectors. (30")arrow_forwardWhat relative orientation of vectors results in a minimum value of magnitude of the cross product? What relative orientation of vectors results in a dot product of zero?arrow_forwardSolve the attached question. Ask's for the dot product, not vector a times vector barrow_forward
- With the given three vector A, B, C. Determine the magnitude of the dot product of vectors AxC and CxB A= 2i - 3j + 4k B= -3i - 6j + 5k C= 4i + 2jarrow_forwardTwo vectors have a magnitude of 3 and 2 and their dot product has a value of -5. Which of the following is the angle between the two vectors? O 146.44 degrees O None of the given choices. O 33.6 degrees O 99.6 degrees O -56.4 degreesarrow_forwardTwo vectors a and b in Figure have equal magnitude of 10 m and the angles are 0, = 30° and 0, = 105°. find the dot product : a.b Oa. -26 O b. 17.4 O. 14.7 O d. 100 Next pagearrow_forward
- Consider the two unit vectors i and k. Give the magnitudes and directions of their dot product.arrow_forwardIn this problem we are going to consider two different examples of the dot product between two vectors, a force F and a displacement delta r.  (a) if the force vector has a magnitude of F= 19 N, The displacement has a length of deltas=1.2 m, and the angle between the vectors is 35°, what will the dot product between the vector F and the vector delta r be? You can answer in Joules (which is the same as Newton meters) . (B) if the force vector has components fx =8.5 N and F y=12 N,  and the displacement factor has components delta rx=0.15 m and delta ry=0.61m, what is the dot product between them? Again, enter the answer in joules. arrow_forwardVectors A and B have scalar product -7.00, and their vector product has magnitude +9.00. What is the angle between these two vectors?arrow_forward
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