AP Physics 1 – Rotation Review Problems

 

1.     A bicycle wheel of diameter 0.74 m is completing 2.5 revolutions per second as the cyclist rides along a level roadway.  (a) Determine the angular speed of the wheel.  (b) Find the linear speed of the cyclist.  (b) If the cyclist applies the brakes and comes to a stop in 3.0 s what is the rate of angular acceleration?

2.     The front door of a certain house is has rotational inertia 5.7 kg m2.  The homeowner notices that if it is set into motion it swings 90.0¡ in 3.0 s before coming to a stop under the influence of only the friction in the hinges.  (a) Determine the amount of torque due to friction.  (b) Given that the door handle is 0.85 m from the hinges, what amount of force acting there must be applied to move the door at constant angular speed?  (c) If a person pulls with a force of 40.0 N on the handle, what will be the rate of angular acceleration?  (d) Challenge:  what amount of force acting on the handle would be enough to open the door 45¡ and shut it again in 2.0 s (starting and stopping at rest without slamming)?

3.     The angular acceleration of the front wheel of a bicycle is caused by the torque generated by friction with the road.  Suppose the wheel has radius 0.370 m and rotational inertia 0.310 kg m2 and that the bicycle accelerates forward at 3.00 m/s2.  (a) Find the angular acceleration of the wheel.  (b) Find the amount of torque that must act on the wheel.  (c) Determine the frictional force that acts on the tread of the front wheel.

4.     Strange as it may sound the friction acting on the rear wheel of the same bicycle from the previous problem is in a forward direction.  However there is also torque being generated by the chain drive and the efforts of the rider.  Assume the total mass of bike, rider, and wheels is 90.0 kg and that the rear wheel has same properties as the front (described previously).  (a) Find the friction acting on the rear wheel – it is responsible for the 3.00 m/s2 forward acceleration of the entire bike and rider system. (Treat as one object.)  (b) Determine the torque of the chain acting on the rear wheel.  (c) Although the tension in the chain is essentially uniform from one end to the other, the torque at each end is dependent on the radius of the gear over which it passes.  Because of this, the torque at the front sprocket is greater than at the rear by a certain factor.  Suppose the gear ratio is 1.2 – what minimum force is required on the front pedal, moving in radius 0.17 m, to accelerate the bike this way?

5.     A wheel of rotational inertia I and diameter D is set spinning by a force F that acts tangentially at the rim over precisely one half of a revolution.  Use the work-energy theorem to derive an expression for the resulting angular speed ω of the wheel in terms of F, D, and appropriate constants.

6.     A solid pulley with rotational inertia I = ½ MR2 has a string wrapped around it and hanging from the end is a small object with mass m.  The object is released from rest – as it moves down the pulley accelerates as the string unwinds without slipping.  The pulley attains an angular speed ω in the process.  Ignore friction.  (a) Use conservation of energy to determine the length L of string that must unwind in terms of m, M, R, ω, and appropriate constants.  (b) Find the acceleration of the falling mass in terms of m, M, R, and appropriate constants.  

7.     The platter on a particular record turntable has mass 750 g, radius 13.0 cm and is running at 33.3 rpm.  A record of mass 225 g and radius 15.2 cm is dropped on the platter.  Use inertia I = ½ MR2 for the both the platter and the record.  (a) If there were no motor or friction what would be the resulting rotation rate of the platter?  (b) What angular impulse must the motor produce to prevent the platter from slowing down?  (c) If the torque of the motor is 0.032 Nm determine the time for the platter to return to its original angular speed.

8.     Sending a spacecraft to Mars is usually accomplished by a Hohmann transfer.  In this technique the spacecraft is launched away from Earth with a speed of 32700 m/s relative to the Sun, along a path tangent to EarthÕs orbit.  The spacecraft then coasts under the sole influence of gravity along an elliptical path that just reaches out to the orbit of Mars.  Use a spacecraft mass of 1500 kg and look up other needed values.  (a) Find the initial angular momentum of the spacecraft relative to the Sun.  (b) Find the speed of the spacecraft arriving at Mars.

 

 

 

1.     a. 16 rad/s
b. 5.8 m/s
c. 5.2 rad/s2

2.     a. 2.0 Nm
b. 2.3 N
c. 5.6 rad/s2
d. 23 N is "enough", 21 N is minimum required!

3.     a. 8.11 rad/s2
b. 2.51 Nm
c. 6.79 N backward

4.     a. 277 N forward
b. 105 Nm
c. 740 N

5.    

6.     a.
b.

7.     a. 23.6 rpm
b. 0.00906 Nms
c. 0.28 s

8.     a. 7.34 × 1018 kg m2/s
b. 21500 m/s