A solid sphere with mass M, radius r, and moment of inertia I is released from rest at the top of a ramp with height h. If the surface of the ramp is frictionless, what is the speed of the center of mass of the solid sphere at the bottom of the ramp? O 2Mghr² I O√2gh 2Mghr² I + Mr² O 2Mghr2 I

A solid sphere with mass M, radius r, and moment of inertia I is released from rest at the top of a ramp with height h. If the surface of the ramp is frictionless, what is the speed of the center of mass of the solid sphere at the bottom of the ramp? O 2Mghr² I O√2gh 2Mghr² I + Mr² O 2Mghr2 I

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter10: Rotational Motion

Section: Chapter Questions

Problem 46P: A playground merry-go-round of radius R = 2.00 m has a moment of inertia I = 250 kg m2 and is...

See similar textbooks

Related questions

Q: Definition of physics

A: Physics is a natural science that involves the study of matter and its motion through spacetime…

Q: The electric field in a sine wave has a peak value of 32.6 mV/m. Calculate the magnitude of the…

A: Given: The strength of the electric field is 32.6 mV/m.

Q: Simple Harmonic Motion The linear graph you should have plotted for the simple pendulum was: T² vs.…

A: The given question is based on the motion of a simple pendulum. We will analyze the given options…

Q: A lens with a focal length, f1 = +1.5 m is attached directly to a second lens with focal length, f2…

Q: A cylinder of diameter 1.0 cm at 300C is to be slide into a hole on a steel plate. The hole has a…

A: diameter of the hole is a linear dimension of the object, which when subjected to heat leads to…

Q: A wooden door (as seen from above) has hinges on the left- hand side. In which direction of the…

Q: In a projectile motion, the velocity is A B C D always perpendicular to the acceleration never…

Q: The ratio of the lateral expansion to the longitudinal shortening of a concrete cylinder when…

A: We need to comment on what we call the ratio of lateral expansion to longitudinal shortening of a…

Q: 1. A string of 50 cm length has a mass of 25 g. What is the linear mass density of the string? a.…

A: linear mass density = mass / length

Q: Mass of crate: 100 kg μk: 0.25 Determine the maximum compression, X. k = 2 kN/m 10 m 45°

Q: Speed of Sound Another student does this lab slightly differently from us; they define "D" as the…

A: Distance between speaker to reflector =D2

Q: An object in a horizontal surface was moved by applying a constant force (In Newtons) F = 8î + 5ĵ.…

Q: The motion of particle is defined by the relation -t-lot² +8t +12, where X and t are expressed in…

A: Given data- The motion of a particle is defined by the relation- x=t4-10t2+8t+12…

Q: The motion of a projectile at affects these kinematic quantities? Below is a figure of the height…

A: Study of the attached graph gives details of height and range of the projectile launched at…

Q: If 40 million Joules of energy is put into the hot reservoir and the engine transfers 22 million…

A: Given Data:- Energy put into the hot reservoir is QH=40 million Joules Energy transfered to the cold…

Q: Current Attempt in Progress An object has a charge of -2.0 μC. How many electrons must be removed so…

A: Given: The initial charge is -2 μC. The final charge is 3.6 μC.

Q: Find the work done Force=12.5 N Displacement=2 m

A: Given data : Displacement=d Force=F Required : Work done

Q: Faraday's law of magnetic induction states that the voltage induced by a current running through a…

Q: The drawing shows six point charges arranged in a rectangle. The value of q is 4.38 µC, and the…

Q: Suppose you use 57 kWh (kilowatt hours) of electricity at $0.35 per kWH, 91 kWh at $0.26 per kWh,…

A: Given, Electricity usage, 57 kWh of electricity at $0.35 per kWh, 91kWh of electricity at $0.26 per…

Q: Solve the given problems. 4. Determine the x, y, z components of reaction at the ball-and-socket…

A: Draw the free-body diagram of the system.

Q: A rubber ball with mass of 150 g is dropped from a height of 2.25 m onto the tiled floor. Graph…

A: Given that:m=150 g=0.150 kghi=2.25 m

Q: 600g of ice at -8℃ is put inside a calorimeter filled with 4000g water initially at 20 ℃. What is…

Q: An airplane acquires a take-off velocity of 150 mph on a 2-mile runway. If the plane started from…

A: Given(s): Initial speed, u=0. Final speed, v=150 mph=150×0.447 m/s=67.05 m/s Covered distance…

Q: An ancient building was known to have been built 3000 years ago. Approximately what proportion of…

A: Given that The age of the ancient building is (T) = 3000year The…

Q: Khufra works at a spring factory and he was assigned to test a spring, whose constant is 50 N/m,…

A: Givenk=50 N/mm=50 kgθ=30°x=0.3 mF=50 N

Q: A generator A employs a magnetic field of 0.10 T and the area of its winding is 0.045 m2.…

Q: Mass of a car is 124 kg, What is it's weight?

A: Given data : Acceleration due to gravity = g Mass of…

Q: Determine momentum Mass=3 kg Velocity=3 m/s

A: Given data : Mass=m Velocity=V Required : Momentum

Q: A 6.0 kg object moving 5.0 m/s [E] collides with and sticks to a 2.0 kg object. After the collision…

A: Given data- Mass m1= 6.0 kg, v1= 5.0 m/s east Mass m2=2.0 kg After collision both the object moves…

Q: Find Density of object of mass 17 kg which accupies space of 0.5 m³

Q: In a physics laboratory experiment, a coil with 200 turns enclosing an area of 11.4 cm² is rotated…

Q: What is the magnetic force that 0.50 m of a current-carrying wire experiences as 3.0 A of current…

Q: Buoyancy In the buoyancy lab, you find that the buoyant force is equal to 2.50 N. Given that the…

Q: Consider a blue ring centered around the m. The ring has 250 nC of charge, a radius of 0.8 m and…

A: charge Q = 250nC Electric field at a distance 15 units from circular ring have to find. The electric…

Q: Review Multiple-Concept Example 4 to see the concepts that are pertinent here. In a television…

A: potential difference = 22000 V

Q: Do forces action and balance reaction pairs of one another ?

A: Given:- 4) Do action and reaction pairs of force balance one another? Explanation:- We know that…

Q: CALC An object's velocity is measured to be U₁(1) = a - Br², where a = 4.00 m/s and ß = 2.00 m/s³.…

A: Motion perpendicular are independent of each other. Motion can be uniform or accelerated. Motion is…

Q: 2. An electron experiences a magnetic force of magnitude 6.95 x 10^-3 N when moving at an angle of…

A: In the given question, Magnetic force (F) = 6.95×10-3N Magnetic field (B) = 1.40T Angle made by the…

Q: A 100g bird is flying with velocity of +3m/s when suddenly it crashes into a giant billboard,…

A: Impulse : Change is momentum is impulse and product of mass into Velocity is momentum. Impulse =…

Q: Sketch a Free Body Diagram (FBD) of the following: 1. A car driving on a highway at a constant speed…

Q: Points A, B, and C are at the vertices of an equilateral triangle. A certain positive field of…

Q: Para el circuito que se muestra en la siguiente figura, use el método que prefiera para encontrar la…

Q: If the mass of the sun was to increase two-fold, what is the effect of this to the gravitational…

A: Mass of earth, mE=6×1024 kgMass of Sun, MS=2×1030 kgDistance between sun and earth, r=1.5×1011 m

Q: Two charges are placed on the x axis. One of the charges (91 = +6.93 μC) is at x₁ = +3.00 cm and the…

A: Given that: q1=6.93×10-6 C at x1=+3.00 cm=+3.00×10-2 mq2=-26.1×10-6 C at x2=+9.00 cm=+9.00×10-2 m

Q: Discussion DEMETOR 1. Explain briefly the Wheatstone bridge principle of operation. 2. List some…

A: 1. Wheatstone bridge is an electrical circuit which is used for calculation of unknown resistance.…

Q: It defines the extent of the system O System O Model O Particle O System Boundart

Q: Force being experienced when it is connected to a spring. Spring Force Compressed Stretched Spring…

Q: Whale and Kanmuro are two islands located at the Chimera archipelago. These two are separated by a…

Q: 600g of ice at -8°C is put inside a calorimeter filled with 4000g water at 20 °C. What is the final…

A: Given data: The mass of ice is m=600 g. The temperature of ice is Ti=-8°C. The mass of water is…

Concept explainers

Torque

Torque is the rotational equivalent of linear force in physics and mechanics. Based on the course of study, it is also known as the moment of force, rotational force, or turning effect.

Question

100%

A solid sphere with mass M, radius r, and moment of inertia I
is released from rest at the top of a ramp with height h. If the
surface of the ramp is frictionless, what is the speed of the
center of mass of the solid sphere at the bottom of the ramp?
h
2Mghr2
I
O√2gh
O
O 2Mghr²
I
2Mghr²
I + Mr²

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step by step

Solved in 5 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

A long, thin rod of mass m = 5.00 kg and length = 1.20 m rotates around an axis perpendicular to the rod with an angularspeed of 3.00 rad/s. a. What is the angular momentum of therod if the axis passes through the rods midpoint? b. What is theangular momentum of the rod if the axis passes through a pointhalfway between its midpoint and its end?
The velocity of a particle of mass m = 2.00 kg is given by v= 5.10 + 2.40 m /s. What is the angular momentumof the particle around the origin when it is located atr= 8.60 3.70 m?
A buzzard (m = 9.29 kg) is flying in circular motion with aspeed of 8.44 m/s while viewing its meal below. If the radius ofthe buzzards circular motion is 8.00 m, what is the angularmomentum of the buzzardaround the center of its motion?
Figure OQ10.6 shows a system of four particles joined by light, rigid rods. Assume a = b and M is larger than m. About which of the coordinate axes does the system have (i) the smallest and (ii) the largest moment of inertia? (a) the x axis (b) the y axis (c) the z axis, (d) The moment of inertia is the same small value for two axes, (e) The moment of inertia is the same for all three axes.
Calculate the moment of inertia of a skater given the following information. (a) The 60.0-kg skater is approximated as a cylinder that has a 0.110-m radius. b) The skater with arms extended is approximated by a cylinder that is 52.5 kg, has a 0.110-m radius, and has two 0.900-m-long arms which are 3.75 kg each and extend straight out from the cylinder like rods rotated about their ends.
A system consists of a disk of mass 2.0 kg and radius 50 cm upon which is mounted an annular cylinder of mass 1.0 kg with inner radius 20 cm and outer radius 30 cm (see below). The system rotates about an axis through the center of the disk and annular cylinder at 10 rev/s. (a) What is the moment of inertia of the system? (b) What is its rotational kinetic energy?
A solid cylinder of mass 2.0 kg and radius 20 cm is rotating counterclockwise around a vertical axis through its center at 600 rev/min. A second solid cylinder of the same mass and radius is rotating clockwise around the same vertical axis at 900 rev/min. If the cylinders couple so that they rotate about the same vertical axis, what is the angular velocity of the combination?
A student sits on a freely rotating stool holding two dumbbells, each of mass 3.00 kg (Fig. P10.56). When his arms are extended horizontally (Fig. P10.56a), the dumbbells are 1.00 m from the axis of rotation and the student rotates with an angular speed of 0.750 rad/s. The moment of inertia of the student plus stool is 3.00 kg m2 and is assumed to be constant. The student pulls the dumbbells inward horizontally to a position 0.300 m from the rotation axis (Fig. P10.56b). (a) Find the new angular speed of the student. (b) Find the kinetic energy of the rotating system before and after he pulls the dumbbells inward. Figure P10.56
A playground merry-go-round of radius R = 2.00 m has a moment of inertia I = 250 kg m2 and is rotating at 10.0 rev/min about a frictionless, vertical axle. Facing the axle, a 25.0-kg child hops onto the merry-go-round and manages to sit down on the edge. What is the new angular speed of the merry-go-round?
A propeller consists of two blades each 3.0 m in length and mass 120 kg each. The propeller can be approximated by a single rod rotating about its center of mass. The propeller starts from rest and rotates up to 1200 rpm in 30 seconds at a constant rate. (a) What is the angular momentum of the propeller at t=10s ; t=20s ? (b) What is the torque on the propeller?
Two astronauts (Fig. P10.67), each having a mass M, are connected by a rope of length d having negligible mass. They are isolated in space, orbiting their center of mass at speeds v. Treating the astronauts as particles, calculate (a) the magnitude of the angular momentum of the two-astronaut system and (b) the rotational energy of the system. By pulling on the rope, one of the astronauts shortens the distance between them to d/2. (c) What is the new angular momentum of the system? (d) What are the astronauts new speeds? (e) What is the new rotational energy of the system? (f) How much chemical potential energy in the body of the astronaut was converted to mechanical energy in the system when he shortened the rope? Figure P10.67 Problems 67 and 68.
A horizontal disk with moment of inertia I1 rotates with angular speed 1 about a vertical frictionless axle. A second horizontal disk having moment of inertia I2 drops onto the first, initially not rotating but sharing the same axis as the first disk. Because their surfaces are rough, the two disks eventually reach the same angular speed . The ratio /l is equal to (a) I1/I2 (b) I2/I1 (c) I1/( I1 + I2) (d) I2/( I1 + I2)