Q: The moment of inertia of a solid sphere about an axis passing through the centre of gravity is 2/5MR…
A: By parallel axis theorem, the moment of inertia at 2R is I = (2MR2/5) + M(2R)2 I = 22MR2/5
Q: The 5.0 MgMg truck and 1.7 MgMg car are traveling with the free-rolling velocities shown just before…
A: a) Using the law of conservation of momentum, mTuT+mCuC=mTvT+mCvC5.0 Mg30 km/h+1.7 Mg10 km/h=5.0…
Q: A tennis ball has a mass of 65 g and a diameter of 6.2 cm. Find the moment of inertia about its…
A: Answer:- Given Mass of a tennis ball (m) = 65 g = 0.065 kg Diameter of the ball(d) = 6.2 cm…
Q: An automobile traveling 65.0 km/h has tires of 60.0 cm diameter. (a) What is the angular speed of…
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Q: An automobile traveling 100 km/h has tires of 72.0 cm diameter. (a) What is the angular speed of the…
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Q: Assume the formula for moment of inertia of a ball is given by I = 2/3Mr^2 What is the radius of…
A: Given data: I = 13.86 kg.m2 Mass (M) = 32.5 kg Need to determine the radius.
Q: 6. Find the angular momentum of Earth around the Sun. Also find the angular momentum of a rod about…
A: Mass , M = 500 gm = 0.5 kg Length , L = 4 m To find = Moment of inertia
Q: Move over Jeff Bezos, this invention is about to make you the richest person in the world. You have…
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Q: Find the centroid (x and y) and the moment of inertia (Ix and Iy) of the given
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Q: Suppose we want to calculate the moment of inertia of a 56.5 kg skater, relative to a vertical axis…
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Q: Calculate the moment of inertia by direct integration of a thin rod of mass M and length L about an…
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Q: An automobile traveling 70.0 km/h has tires of 73.0 cm diameter. (a) What is the angular speed of…
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Q: Determine the moment of inertia of a solid sphere of mass 64kg and radius 65.8cm about an axis that…
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Q: what is the sphere's radius
A: Given radius of the cylinder (r)= 4.9cm radius of the sphere =R the mass of both sphere and…
Q: A discus thrower moves the discus in 2.40 complete revolutions about his body in 1.43 s (starting…
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Q: Starting from rest, a disk rotates about its central axis with constant angular acceleration. In…
A: d) The angular acceleration from the first part is calculated as 1.656 rad/s2.
Q: (a) Calculate the magnitude of the angular momentum of the earth in a circular orbit around the sun.…
A: Given data M=5.97×1024 kgR=6.38×106 mr=1.5×1011 mT=365 days
Q: Calculate the moment of inertia of a hollow sphere of mass M and radius R about its diameter.
A: In order to determine the moment of inertia of hollow sphere (mass=M, radius=R) about its diameter,…
Q: Answer the question in full details, thank you very much, Answer on the correct significant figures:…
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(a) Determine the centroidal polar moment of inertia of a circular area by direct integration. (b) Using the result of part (a), determine the moment of inertia of a circular area with respect to a diameter.
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- Consider a stick 1.00 m long and its moments of inertia about axes perpendicular to the stick's length and passing through two different points on the stick: first, a point at its center and second, a point 17 cm from one end. Calculate the ratio I2/11, the ratio of the second moment of inertia to the first. SE || Record your numerical answer below, assuming three significant figures. Remember to include a "-" as necessary.= [7.] The moment of inertia of a solid sphere is I = mr². The moment of inertia of a ring is I mr². A sphere and a ring with equal masses (m) and equal radii r both roll up an inclined plane. They start with the same linear velovity v for the center of mass. (a) Without doing a calculation, clearly explain which will go higher. (b) Use conservation of energy to determine the maximum vertical height h the sphere and the ring will reach.A thin uniform disc of mass M and radius R has con- centric hole of radius r. Find the moment of inertia of the disc about an axis passing through its centre and perpendicular to its plane.
- Formula 1 cars have tires with a diameter of 72 cm. For this problem, we will consider the case of the car traveling in a straight line at a speed of 324 km/hr. (a) What is the angular velocity of the tires? Number (b) What is the centripetal acceleration at the edge of the tire? Number rad/s Number (c) If a bacterium (m = 1.50 x 10-15 kg) clings to the edge of the tire, what force must the bacterium exert to stay on the edge of the tire? m/s² Number N (d) Take the ratio of this force to the bacterium's weight. For your own consideration: Is this answer surprising? Could a human perform the same feat? Why might a bacterium be able to do that?Moment of inertia Derive the formula for the moment of inertia of a uniform thin rod of length L and mass M about an axis through its center, perpendicular to its face. Repeat the calculation, only now assume the rod has a density that increases uniformly from a value of po on one end to 2po on the other end. Suggestion For the second integration, it is important to define the density function correctly: It will be a straight line that includes the two points (-L/2, po) and (L/2, 2po). Find the slope of the line as rise of run, and the x-intercept, p(0). Total mass of the rod, M, will be the integral of the density function from -L/2 to L/2. If you solve the second integration correctly, including the value of the total mass, M, in terms of p, you should see a very interesting relationship between the two moments of inertia.10. Ā = -2â + -3ŷ and B = -4â + -4ŷ. Calculate R = Ã+B. Calculate 0, the direction of R. Recall that 0 is defined as the angle with respect to the +x-axis. A. 49.4° B. 130.6° C. 229.4° D. 310.6°
- An automobile traveling 70.0 km/h has tires of 64.0 cm diameter. (a) What is the angular speed of the tires about their axles? (b) If the car is brought to a stop uniformly in 25.0 complete turns of the tires, what is the magnitude of the angular acceleration of the wheels? (c) How far does the car move during the braking? (Note: automobile moves without sliding) (a) Number i Units (b) Number i Units (c) Number i UnitsAn automobile traveling 85.0 km/h has tires of 78.0 cm diameter. (a) What is the angular speed of the tires about their axles? (b) If the car is brought to a stop uniformly in 21.0 complete turns of the tires, what is the magnitude of the angular acceleration of the wheels? (c) How far does the car move during the braking? (Note: automobile moves without sliding) (a) Number Units (b) Number i Units (c) Number i Units >Determine the moment of inertia of a solid homogeneous cylinder of radius R and length L with respect to a diameter in the base of the cylinder.
- The object shown below is centered on the origin, and has a width of 20 cm in the x direction, 3 cm in the y direction, and 5 cm in the z direction. Around which axis does it have the lowest moment of inertia l?An automobile traveling 110 km/h has tires of 69.0 cm diameter. (a) What is the angular speed of the tires about their axles? (b) If the car is brought to a stop uniformly in 21.0 complete turns of the tires, what is the magnitude of the angular acceleration of the wheels? (c) How far does the car move during the braking? (Note: automobile moves without sliding) (a) Number i Units (b) Number i Units (c) Number i UnitsFind the moment of inertia for a solid cube is bounded by planes x = F1, z = 71 , y = 3 and y = 5 about x – axis