Rotational Kinematics
Rotational Dynamics
Quantities (timed)
Energy & Momentum
Grab Bag (timed)
100
- What would happen to an object with no tangential acceleration but a nonzero radial acceleration.
- What would happen to an object with no radial acceleration but a nonzero tangential acceleration.
- spin in a circle at a constant rate
- accelerate in a straight line, never going in a circle
100
Rank the following from largest torque to smallest torque, assuming the force of each is the same.
1 > 3 > 4
100
Symbol and units – in order – of angular velocity, angular acceleration, angular displacement.
angular velocity - omega - rad/s
angular acceleration - alpha - rad/s^2
angular displacement - delta theta - rad
100
Which has more kinetic energy: a rolling disk or a rolling hoop? Assume they have the same radius, mass, and translational velocity.
disk = 1/2(1/2 m r^2) (v/r)^2 + 1/2 m v^2 = 3/4 mv^2
hoop = 1/2 ( mr^2)(v/r)^2 + 1/2 m v^2 = m v^2
hoop has more KE
100
If you double a flywheel’s rotational speed, by what factor will its rotational acceleration increase?
KE = 1/2 I w^2
4 times as much
200
Bonnie sits on the outer rim of a merry-go-round, and Klyde sits midway between the center and the rim (at r/2). Bonnie has an angular velocity of 12 rad/s and tangential velocity of 10 m/s. Calculate Klyde’s rotational and tangential velocity.
Klyde's rotational is still 12 rad/s.
Klyed's tangential velocity is 5 m/s.
200
When a tape is played on a cassette deck, there is a tension in the tape that applies a torque to the supply reel. Assuming the tension remains constant during playback, how does this applied torque vary as the supply reel becomes empty?
torque decreases as time goes on.
200
Symbol and units of angular momentum.
L - kg m^2/s
200
Two different spinning disks have the same angular velocity, but disk 1 has more kinetic energy than disk 2. Which one has the bigger moment of inertia? Why?
KE = 1/2 I w^2
They have the same w. So in order for 1 to have more KE, it has to have more I.
200
You are holding a spinning bicycle wheel (spinning counter clockwise) while standing on a stationary turntable. If you suddenly flip the wheel over so that it is spinning clockwise, the turntable will do what?
spin counter clockwise
(The total angular momentum of the system is L upward, and it is conserved. So if the wheel has
-L downward, you and the table must have +2L upward.)
300
Calculate the rotational velocity needed on wheel A in order to make wheel B achieve a rotational velocity of 250 rpm. Assume the radius of A is 30 cm and the radius of B is 50 cm.
417 rpm
300
Rank the following from largest torque to smallest torque, assuming the force on each nut is the same. (Hint: two are tied)
2 > 1 = 4 > 3
300
Convert 300 rpm to rad/s
31.4 rad/s
300
Why does an ice skater spin faster when she pulls her arms in?
radius is smaller, so I is smaller. This leads to a larger w
300
A solid cylinder of radius 20 cm and a solid sphere of radius 35 cm are released at the same time from the top of a ramp. Which will reach the bottom first?
sphere has I = 2/5 mr^2. Cylinder has I = 1/2 mr^2. Relatively speaking, sphere has less fraction of inertial moment, so it will be more affected by gravity and hit the ground first.
400
Suppose that the speedometer of a truck is set to read the linear speed of the truck, but uses a device that actually measures the angular speed of the tires. If larger diameter tires are mounted on the truck instead, how will that affect the speedometer reading as compared to the true linear speed of the truck? Explain.
the speedometer will read too slow. Every revolution, the tire will have traveled farther than expected. Therefore, it will be travelling faster than the speedometer expects.
Alternative explanation: The linear speed is v = wR. So when the speedometer measures the same angular speed w as before, the linear speed v is actually higher, because the tire radius is larger than before.
400
Two spheres have the same radius and equal masses. One is made of solid aluminum, and the other is made from a hollow shell of gold. Which one has the bigger moment of inertia? Explain.
hollow shell of gold has more I because more of its mass is at a larger radius
400
Symbol and units – in order – of torque, moment of inertia, rotational kinetic energy
torque = tau = mN
moment of inertia = I = kg m^s
rotational KE = KE_r = Joules
400
A force is applied to a dumbbell for a certain period of time, first as in (a) and then as in (b). In which case does it acquire more kinetic energy? Explain.
(a) has translational KE
(b) has translational + rotational KE, so it has more
400
Rank from largest to smallest angular momentum. There may be ties
- A hollow cylinder of mass M and radius R and angular speed ω.
- A solid cylinder of mass M and radius R and angular speed ω.
- A solid cylinder of mass M and radius 2R and angular speed ω.
- A hollow cylinder of mass M and radius R and angular speed 2ω.
4 = 3 > 1 > 2