Torques and Moments of Force
What is the SI unit for torque?
Nm
What is the direction of the angular velocity of a shotputter if they are spinning in a clockwise direction prior to releasing the shot?
Negative
What term describes how far an object rotates, measured in degrees or radians?
Angular displacement
What property depends on how an object’s mass is distributed relative to its axis of rotation?
Moment of inertia
What rotational quantity is the product of torque and the time over which it is applied?
Angular impulse
Name one movement that would raise your center of gravity?
Any upward movement (i.e., lifting arm up, getting on your tiptoes, etc.)
What is the primary plane of motion for an athlete performing squats?
Sagittal (median) plane
A baseball player swings a bat through 90° in 0.5 seconds. What happens to the average angular velocity if the same swing is completed in 0.25 seconds?
It doubles
Which of Newton's laws states that for every torque exerted by one object on another, the other object exerts an equal but opposite torque on the first object.
Newton's Third Law
A wrestler in a low, wide stance is manipulating his center of gravity to increase which of the following?
a. Power
b. Speed
c. Stability
d. Torque
c. Stability
How many degrees are in 17 radians?
974 degrees
What is the component of angular acceleration that directly contributes to an object’s linear velocity at release?
Tangential acceleration
If the radius of gyration of an object increases, how does this affect its resistance to rotation?
It becomes more difficult to rotate
A gymnast brings in her arms and legs during a spin to increase her rotation. What happens to her angular velocity and moment of inertia?
Angular velocity increases, moment of inertia decreases
What is the perpendicular distance between the axis of rotation and the line of action of the force?
Moment arm
During a cartwheel, around which axis does the gymnast primarily rotate?
Anteroposterior axis
While performing a backflip on a trampoline, around which axis is the person rotating?
Transverse axis
A diver has a moment of inertia of 4.2 kg·m² and an angular velocity of 3.0 rad/s. What is her angular momentum?
12.6 kg·m²/s
H = I × ω = 4.2 × 3.0
A hockey player uses a hockey stick that weighs 0.4 kg. The player applies an average torque of 40 N·m to their stick for 0.3 seconds. What is the angular impulse?
12 Nm s
Angular impulse = T × t = 40 × 0.3
A weightlifter holds a 10 kg weight 0.4 m from her shoulder joint. Calculate the torque produced by the weight about the shoulder.
39.2 Nm
T = F x r = (10 x 9.81) x 0.4
A baseball bat rotates through 120° in 0.25 seconds. What is the average angular velocity in radians per second?
8.4 rad/s
ω = Δθ / Δt = (120 × π/180) / 0.25
A figure skater spins from rest to an angular velocity of 12 rad/s in 3 seconds. What is the angular acceleration?
4 rad/s^2
α = Δω / Δt = (12 − 0) / 3
A discus thrower applies a torque of 60 N·m to a discus with a moment of inertia of 2.5 kg·m². What is the angular acceleration?
24 rad/s²
α = T / I = 60 / 2.5 = 24 rad/s²
A gymnast has an angular momentum of 24 kg·m²/s. If her moment of inertia is 3 kg·m², what is her angular velocity?
8 rad/s
H = Iω → ω = 24 / 3