Rotation
What determines how difficult it is to change an object’s rotational motion?
What is moment of inertia?
What must be true for angular momentum to be conserved?
What is no net external torque?
What defines simple harmonic motion in terms of force and displacement?
What is restoring force proportional to displacement?
What determines whether an object floats in a fluid?
What is density relative to the fluid?
What is the relationship between linear and angular speed?
What is v = rω?
A force is applied closer to the axis. How does torque change?
What is torque decreases?
A solid cylinder rolls without slipping. Identify the form(s) of energy/energies of the cylinder.
What is translational KE (½mv²) and rotational KE (½Iω²)?
If amplitude doubles, compare the changes in maximum speed and total energy.
What is max speed doubles; energy increases by factor of 4?
Why does pressure increase with depth in a fluid?
What is P = ρgh?
If net torque on an object is zero, what can you say about its rotational motion?
What is angular velocity is constant?
Two objects have the same mass but different shapes. When released down a ramp, one reaches the bottom first. Why?
What is the winning object has a lower moment of inertia?
A rotating object doubles its angular speed. How does its rotational kinetic energy change?
What is increases by a factor of 4?
At what position in SHM is speed maximum, and why?
What is at equilibrium; all energy is kinetic?
Water flows from a pipe of area 2 m² into 1 m². If initial speed is 3 m/s, what is final speed?
What is 6 m/s?
A pendulum’s period depends on which variables?
What is length and gravity?
A point on a rotating disk is 0.4 m from the center and the disk rotates at 5 rad/s. What is its linear speed?
What is 2 m/s?
A figure skater pulls in their arms. Explain what happens to the moment of inertia, angular speed, and rotational kinetic energy.
What is I decreases, ω increases, KE increases?
A spring system has k = 100 N/m and m = 1 kg. What is angular frequency?
What is 10 rad/s?
Explain why fluid pressure decreases as speed increases.
What is energy conservation (Bernoulli): faster flow → lower pressure?
A solid cylinder of mass 2.0 kg and radius 0.50 m rolls without slipping down a ramp. At a certain point, its center of mass has a speed of 4.0 m/s. What is the total kinetic energy of the cylinder at that point?
What is KEtotal = 24 J?
A disk starts from rest and rotates with constant angular acceleration. Describe how angular velocity and angular displacement change over time.
What is ω increases linearly; angular displacement increases quadratically
A ball of mass 1.2 kg and radius 0.2 m is released from rest at the top of a 3 m hill. It rolls down the hill without slipping. Determine the translational speed of the ball at the bottom of the hill.
What is vf = 6.48 m/s?
A 0.50 kg mass is attached to a spring with spring constant 200 N/m. The mass is pulled 0.10 m from equilibrium and released from rest. What is the speed of the mass when it is 0.05 m from equilibrium?
What is vf = 1.73 m/s?
Water flows through a horizontal pipe that narrows from a cross-sectional area of 0.040 m² to 0.010 m². The pressure in the wider section is 2.0 × 10⁵ Pa, and the speed of the water there is 2.0 m/s. What is the pressure in the narrower section?
What is P2 = 1.7 x 105 Pa?
A fluid speeds up as it enters a narrower region of pipe. Using conservation principles, explain what must happen to pressure and why.
What is pressure decreases due to conservation of energy (Bernoulli) and continuity?