Exam 8: Rotational Equilibrium and Rotational Dynamics

A circular disk is rotating about a central axis with an angular velocity which is increasing at a constant rate.Point 1 on the disk is located at a distance From the center of the disk and point 2 on the disk is located at a distance From the center of the disk.If ,which of the following ratios is the largest? 1 and 2 refer to being at points 1 and 2 in the subscripts below,all values occurring at the same time.

Suppose a car has a 100,000 mile 10 year warranty on the wheels and axles of a car.How may turns will the wheels of 0.70-m diameter make if both the mileage and time warranties run out simultaneously and what will be the average angular velocities of the wheel? (Assume that a mile = 1.6 x 10³ M and that a year is 3.16 x 10⁷ S)

A majorette takes two batons and fastens them together in the middle at right angles to make an "x" shape.Each baton was 0.60 m long and each ball on the end is 0.10 kg.(Ignore the mass of the rods. )What is the moment of inertia if the arrangement is spun around an axis formed by one of the batons?

A 4.0-kg mass is placed at (2.0,3.0)m,and a 7.0-kg mass is placed at (2.0,−3.0)m.What is the moment of inertia of this system of masses about the y axis?

A majorette takes two batons and fastens them together in the middle at right angles to make an "x" shape.Each baton was 0.90 m long and each ball on the end is 0.20 kg.(Ignore the mass of the rods. )What is the moment of inertia if the arrangement is spun around an axis through the center perpendicular to both rods?

An automobile accelerates from zero to 56 m/s in 7 s.The wheels have a diameter of 2 m.What is the average angular acceleration of each wheel?

A baseball pitcher loosens up his pitching arm.He tosses a 0.15-kg ball using only the rotation of his forearm,0.26 m in length,to accelerate the ball.If the ball starts at rest and is released with a speed of 23 m/s in a time of 0.4 s,what torque is applied to the ball while being held by the pitcher's hand to produce the angular acceleration?

Two children seat themselves on a seesaw.The one on the left has a weight of 300 N while the one on the right weighs 200 N.The fulcrum is at the midpoint of the seesaw.If the child on the right is not at the end but is 2.00 m from the fulcrum and the seesaw is balanced,what is the torque provided by the weight of the child on the left? (Take ccw as positive. )

A ceiling fan is turned on and reaches an angular speed of 110 rev/min in 20 s.It is then turned off and coasts to a stop in an additional 60 s.The ratio of the average angular acceleration for the first 20 s to that for the last 60 s is which of the following?

A uniform meterstick balances on a fulcrum placed at the 60-cm mark when a weight W is placed at the 20-cm mark.What is the weight of the meterstick?

If a nonzero torque is applied to an object,that object will experience:

A 0.300-kg object is swung in a circular path and in a vertical plane on a 0.500-m length string.If the angular speed at the bottom is 4.00 rad/s,what is the tension in the string when the object is at the bottom of the circle?

A spool of thread has an average radius of 1.00 cm.If the spool contains 142 m of thread,how many turns of thread are on the spool? "Average radius" allows us to not need to treat the layering of threads on lower layers.

A meterstick is supported by a knife-edge at the 50-cm mark.Doug hangs masses of 0.40 and 0.80 kg from the 15-cm and 80-cm marks,respectively.Where should Doug hang a third mass of 0.20 kg to keep the stick balanced?

A uniform rod of length L and weight W is placed on a fulcrum a distance of 0.2L from the left end.On the left end is placed a mass of weight 3W and on the right end a vertical force F is applied to keep the system in balance.What are the magnitude and direction of the force F? ​

A 0.400-kg rock is swung in a circular path and in a vertical plane on a 0.25-m length string.At the top of the path,the angular speed is 12.0 rad/s.What is the tension in the string at that point?

A 0.50-m radius automobile tire accelerates from rest at a constant 4.0 rad/s² over a 6.0 s interval.What is the tangential component of acceleration for a point on the outer edge of the tire during the 6.0-s interval?

Which of the first units given below can be units for angular acceleration while the second units can be units for angular velocity?

A 0.21-m radius grinding wheel takes 2.2 s to speed up from 4.0 rad/s to 13.0 rad/s.What is the wheel's average angular acceleration?

Calculate the linear speed due to the Earth's rotation for a person at a point on its surface located at 70^o N latitude.The radius of the Earth is 6.40 × 10⁶ m.