Torque and Equilibrium
What is the unit for torque?
N m or Newton metre
How do we calculate an object's moment of inertia?
Splitting the body into tiny, pinpoint, bits.
What does Newton´s second law translate into when applied to rotational motion?
τ=Iα
What is the formula for calculating work (W) done by a force (F) acting along a displacement (d) at an angle (θ) to the direction of displacement?
W=Fdcos(θ)
What is the formula for calculating the angular momentum (L) of a rotating object with a moment of inertia (I) and angular velocity (ω)?
L=Iω
Define, rotational and translational equilibrium.
TE: The net force is zero or F1 + F2 = FN
RE: The net torque is zero.
An arrow is fired out of a bow, and in the air, it begins spinning along its longest axis. At the very point of the arrow´s head, what is the moment of inertia?
0
A disk with a moment of inertia of 0.5 kg⋅m2 is subjected to a net torque of 2 N⋅m. What is the angular acceleration of the disk?
Equation:
τ=Iα
4rad/s2
How much work is done by a 10N force moving an object 5m horizontally?
W=Fdcos(θ)
50J
What is the angular momentum of a disk with a moment of inertia of 0.2kg⋅m2 rotating at 10rad/s?
L=Iω
2kg⋅m2⋅s-1
Two forces applied in different directions of magnitude, F, and 2F, are acting on a body. both vectors pass through the axis of rotation of the body at different angles. Which direction is the body more likely to rotate to?
Neither, the force vectors both pass through the axis of rotation and will therefore not produce any torque.
In a rotating disk, every point has what linear velocity?
Every point has a different linear velocity.
A solid sphere of radius 0.2 m and mass 2 kg is rolling without slipping. If a torque of 0.4 N⋅m is applied to it, what is the sphere's angular acceleration?
12.5rad/s2
What is the power output of a motor that does 600J of work in 10s?
P=W/t
60W
A figure skater with a moment of inertia of 5kg⋅m2 increases her spin rate from 0rad/s to 6rad/s in 2s. What is the change in her angular momentum?
L=Iω
3kg⋅m2⋅s-1
The same force, F=20N, is applied to a metal rod, length 6 meters, with different force angles to the rotation axis. The angles are θ=90º, θ=50º, and θ=33º. Which angle will provide the highest torque?
Equation:
τ=Fr sinθ
The force applied at an angle of 90º will result in the highest torque. τ=120N m
A ring, with a moment of inertia MR2, of mass 0.45kg and radius of 0.20m rotates with an angular velocity of 5.2 rad-1. Calculate its Kinetic Energy.
Ek=0.24J, I= 1.8 * 10-2
A solid cylinder with a moment of inertia of 0.5⋅m2 achieves an angular acceleration of 10rad/s2. What torque was applied to the cylinder?
5N⋅m
A car accelerates from rest to 20m/s in 5s. If the total work done by the engine is 10,000J, what is the average power output?
P=W/t
2,000W
A rotating wheel has an angular momentum of 120kg⋅m2⋅rad/s and a moment of inertia of 15kg⋅m2. What is its angular velocity?
L=Iω
8rad/s
Two people on a sea-saw sat apart at distances, r1=0.6, and r2=1.4 to the normal, trying to balance the sea-saw perfectly horizontally. Person one is applying a force of F2=360N. What is the normal force acting on the sea-saw?
Equations:
FN=550N
The equation, Mgh = (1/2) Mv2 + (1/2) I ω2, can be used to calculate a cylinder's linear speed as it rolls without slipping down a straight decline and changes altitude by a height 'h'. Will the speed be higher or lower if the cylinder was a point particle?
higher, explanation needed for points.
A uniform rod of length 2 m and mass 4 kg is pivoted at one end. If it is to be rotated from rest to an angular displacement of π/2rad in 2 s with uniform angular acceleration, what is the required torque?
Equations:
I=(1/3)m(l)2
θ=1/2αt2
(8π/3)N⋅m
A cyclist climbs a 100 m hill over a distance of 500 m. If the total work done against gravity is 9,000 J, what is the average force exerted by the cyclist?
F=W/d
18N
A gymnast in a spin has an initial angular velocity of 5rad/s and a moment of inertia of 0.1kg⋅m2. If she pulls in her arms and reduces her moment of inertia to 0.05kg⋅m2, what is her new angular velocity, assuming no external torques?
L=Iω
3kg⋅m2⋅s-1