4) Rolling without slipping A cylindrical wheel of uniform density with mass M= 11kg and radius R= 2m rolls without slipping on an incline that makes an angle of 0 = 30° with the horizontal, as shown in the diagram; there is friction between the wheel and the ramp. A block of equal mass Mis sliding on a separate, frictionless incline, also forming an angle of 0 = 30° with the horizontal. A thin, ideal rope tied to the block passes over an ideal pulley near the peak between the two ramps, and wraps around the outside of the rolling wheel; the rope is parallel to the ramp on each side of the apparatus. Recall that the moment of inertia of a cylinder about its axis of symmetry is Iem = 2MR2. Recall that sin(30°) = 2 and cos(30°) 0.9. a) Draw 2 separate "extended" free body diagrams, one for the block and one for the wheel, indicating where every force acts on each of these objects. b) What is the magnitude of the normal force acting on the wheel? c) If the wheel were to roll a distance of 1 m down the ramp, then how far would the block slide during that time? M. friction d) What is the acceleration of the block? Clearly indicate whether it accelerates up or down the incline. no friction e) What is the tension in the rope?

4) Rolling without slipping A cylindrical wheel of uniform density with mass M= 11kg and radius R= 2m rolls without slipping on an incline that makes an angle of 0 = 30° with the horizontal, as shown in the diagram; there is friction between the wheel and the ramp. A block of equal mass Mis sliding on a separate, frictionless incline, also forming an angle of 0 = 30° with the horizontal. A thin, ideal rope tied to the block passes over an ideal pulley near the peak between the two ramps, and wraps around the outside of the rolling wheel; the rope is parallel to the ramp on each side of the apparatus. Recall that the moment of inertia of a cylinder about its axis of symmetry is Iem = 2MR2. Recall that sin(30°) = 2 and cos(30°) 0.9. a) Draw 2 separate "extended" free body diagrams, one for the block and one for the wheel, indicating where every force acts on each of these objects. b) What is the magnitude of the normal force acting on the wheel? c) If the wheel were to roll a distance of 1 m down the ramp, then how far would the block slide during that time? M. friction d) What is the acceleration of the block? Clearly indicate whether it accelerates up or down the incline. no friction e) What is the tension in the rope?

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter10: Rotational Motion And Angular Momentum

Section: Chapter Questions

Problem 17PE: An automobile engine can produce 200 N m of torque. Calculate the angular acceleration produced if...

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An automobile engine can produce 200Nm of torque. Calculate the angular acceleration produced if 95.0 of this torque is applied to the drive shaft, axle, and rear wheels of a car, given the following information. The car is suspended so that the wheels can turn freely. Each wheel acts like a 15.0-kg disk that has a 0.180-m radius. The walls of each tire act like a 2.00-kg annular ring that has inside radius of 0.180 m and outside radius of 0.320 m. The tread of each tire acts like a 10.0-kg hoop of radius 0.330 m. The 14.0-kg axle acts like a rod that has a 2.00-cm radius. The 30.0-kg drive shaft acts like a rod that has a 3.20-cm radius.
Calculate the rotational kinetic energy in the motorcycle wheel (Figure 10.38) if its angular velocity is 120 rad/s. Assume M=12.0kg,R1=0.280m, and R2=0.330m .
A potters wheela thick stone disk of radius 0.500 in and mass 100 kgis freely rotating at 50.0 rev/min. The potter can stop the wheel in 6.00 s by pressing a wet rag against the rim and exerting a radially inward force of 70.0 N. Find the effective coefficient of kinetic friction between wheel and rag.
If global warming continues, its likely that some ice from the polar ice caps of the Earth will melt and the water will be distributed closer to the equator. If this occurs, would the length of the day (one rotation) (a) increase, (b) decrease, or (c) remain the same?
A grindstone with a mass of 50 kg and radius 0.8 m maintains a constant rotation rate of 4.0 rev/s by a motor while a knife is pressed against the edge with a force of 5.0 N. The coefficient of kinetic friction between the grindstone and the blade is 0.8. What is the power provided by the motor to keep the grindstone at the constant rotation rate?
CHECK and THINK Our results give us a way to think about how a person might steer a unicycle. Consider the person, the unicycle, and the Earth as the system. No net torque acts on the system. Ignoring the motion of the Earth, Figure 13.37A shows the initial angular momentum of the system with the unicycle in motion: Li=Ltire. The person leans to his left so that the angular momentum of the tire rotates downward. The total angular momentum must still point to the right (Fig. 13.37B), so the angular momentum of the person must be upward to compensate. The persons angular velocity therefore points upward (parallel to his own angular momentum), and he is able to make a turn. Another way to analyze this situation is to exclude the Earth from the system and calculate the torque done by gravity. This approach is left as a homework problem. FIGURE 13.37 C Reanalyze the unicycles motion in Example 13.15 (page 382). This time, leave the Earth out of the system and explain how the torque exerted by gravity causes the unicycle to turn. Your explanation should involve a diagram.
Calculate the rotational kinetic energy of a 12-kg motorcycle wheel if its angular velocity is 120 rad/s and its inner radius is 0.280 m and outer radius 0.330 m.
A cylinder of mass 10.0 kg rolls without slipping on a horizontal surface. At a certain instant, its center of mass has a speed of 10.0 m/s. Determine (a) the translational kinetic energy of its center of mass, (b) the rotational kinetic energy about its center of mass, and (c) its total energy.
A 60.0-kg woman stands at the rim of a horizontal turntable having a moment of inertia of 500 kg m2 and a radius of 2.00 m. The turntable is initially at rest and is free to rotate about a frictionless, vertical axle through its center. The woman then starts walking around the rim clock-wise (as viewed from above the system) at a constant speed of 1.50 m/s relative to Earth. (a) In what direction and with what angular speed does the turntable rotate? (b) How much work does the woman do to set herself and the turntable into motion?
An automobile engine can produce 200 N m of torque. Calculate the angular acceleration produced if 95.0% of this torque is applied to the drive shaft, axle, and rear wheels of a car, given the following information. The car is suspended so that the wheels can turn freely. Each wheel acts like a 15.0 kg disk that has a 0.180 m radius. The walls of each tire act like a 2.00-kg annular ring that has inside radius of 0.180 m and outside radius of 0.320 m. The tread of each tire acts like a 10.0-kg hoop of radius 0.330 m. The 14.0-kg axle acts like a rod that has a 2.00-cm radius. The 30.0-kg drive shaft acts like a rod that has a 3.20-cm radius.
The Earth has more rotational kinetic energy now than did the cloud of gas and dust from which it formed. Where did this energy come from? Figure 10.33 An immense cloud of rotating gas and dust contracted under the influence of gravity to form the Earth and in the process rotational kinetic energy Increased. (credit: NASA)
Describe how work is done by a skater pulling in her arms during a spin. In particular, identify the force she exerts on each arm to pull it in and the distance each moves, noting that a component of the force is in the direction moved. Why is angular momentum not increased by this action?