01. Angular Displacement, Velocity and Acceleration
Rotational Motion

149856 Three particles \(A, B, C\) are situated at the vertices of an equilateral triangle \(A B C\) of side \(d\) at \(\mathbf{t}=0\). Each of the particles moves with constant speed \(v\). A always has its velocity along \(A B, B\) along \(B C\) and \(C\) along \(C A\). The time the particles meet each other is

1 \(\mathrm{d} /(3 \mathrm{v})\)
2 \(2 \mathrm{~d} /(3 \mathrm{v})\)
3 \(3 \mathrm{~d} /(2 \mathrm{v})\)
4 \(d / v\)
Rotational Motion

149857 A particle executing SHM has a maximum speed of \(0.5 \mathrm{~ms}^{-1}\) and maximum acceleration of \(1.0 \mathrm{~ms}\) . The angular frequency of oscillation is:

1 \(2 \mathrm{rad} \mathrm{s}^{-1}\)
2 \(0.5 \mathrm{rad} \mathrm{s}^{-1}\)
3 \(2 \pi \mathrm{rad} \mathrm{s}^{-1}\)
4 \(0.5 \pi \mathrm{rad} \mathrm{s}^{-1}\)
Rotational Motion

149859 A rotating wheel changes angular speed from \(1800 \mathrm{rpm}\) to \(3000 \mathrm{rpm}\) in 20s. What is the angular acceleration assuming to be uniform?

1 \(60 \pi \mathrm{rad} \mathrm{s}^{-2}\)
2 \(90 \pi \mathrm{rad} \mathrm{s}^{-2}\)
3 \(2 \pi \mathrm{rad} \mathrm{s}^{-2}\)
4 \(40 \pi \mathrm{rad} \mathrm{s}^{-2}\)
Rotational Motion

149860 When a ceiling fan is switched off, its angular velocity reduces by \(50 \%\) while it makes 36 rotations. How many more rotation will it make before coming to rest? (Assume uniform angular retardation):

1 36
2 48
3 18
4 12
Rotational Motion

149861 How much revolution does the engine make during the time when a motor wheel with angular speed is increased from \(720 \mathrm{rpm}\) to \(2820 \mathrm{rpm}\) in 14 seconds?

1 354
2 490
3 413
4 620
Rotational Motion

149856 Three particles \(A, B, C\) are situated at the vertices of an equilateral triangle \(A B C\) of side \(d\) at \(\mathbf{t}=0\). Each of the particles moves with constant speed \(v\). A always has its velocity along \(A B, B\) along \(B C\) and \(C\) along \(C A\). The time the particles meet each other is

1 \(\mathrm{d} /(3 \mathrm{v})\)
2 \(2 \mathrm{~d} /(3 \mathrm{v})\)
3 \(3 \mathrm{~d} /(2 \mathrm{v})\)
4 \(d / v\)
Rotational Motion

149857 A particle executing SHM has a maximum speed of \(0.5 \mathrm{~ms}^{-1}\) and maximum acceleration of \(1.0 \mathrm{~ms}\) . The angular frequency of oscillation is:

1 \(2 \mathrm{rad} \mathrm{s}^{-1}\)
2 \(0.5 \mathrm{rad} \mathrm{s}^{-1}\)
3 \(2 \pi \mathrm{rad} \mathrm{s}^{-1}\)
4 \(0.5 \pi \mathrm{rad} \mathrm{s}^{-1}\)
Rotational Motion

149859 A rotating wheel changes angular speed from \(1800 \mathrm{rpm}\) to \(3000 \mathrm{rpm}\) in 20s. What is the angular acceleration assuming to be uniform?

1 \(60 \pi \mathrm{rad} \mathrm{s}^{-2}\)
2 \(90 \pi \mathrm{rad} \mathrm{s}^{-2}\)
3 \(2 \pi \mathrm{rad} \mathrm{s}^{-2}\)
4 \(40 \pi \mathrm{rad} \mathrm{s}^{-2}\)
Rotational Motion

149860 When a ceiling fan is switched off, its angular velocity reduces by \(50 \%\) while it makes 36 rotations. How many more rotation will it make before coming to rest? (Assume uniform angular retardation):

1 36
2 48
3 18
4 12
Rotational Motion

149861 How much revolution does the engine make during the time when a motor wheel with angular speed is increased from \(720 \mathrm{rpm}\) to \(2820 \mathrm{rpm}\) in 14 seconds?

1 354
2 490
3 413
4 620
Rotational Motion

149856 Three particles \(A, B, C\) are situated at the vertices of an equilateral triangle \(A B C\) of side \(d\) at \(\mathbf{t}=0\). Each of the particles moves with constant speed \(v\). A always has its velocity along \(A B, B\) along \(B C\) and \(C\) along \(C A\). The time the particles meet each other is

1 \(\mathrm{d} /(3 \mathrm{v})\)
2 \(2 \mathrm{~d} /(3 \mathrm{v})\)
3 \(3 \mathrm{~d} /(2 \mathrm{v})\)
4 \(d / v\)
Rotational Motion

149857 A particle executing SHM has a maximum speed of \(0.5 \mathrm{~ms}^{-1}\) and maximum acceleration of \(1.0 \mathrm{~ms}\) . The angular frequency of oscillation is:

1 \(2 \mathrm{rad} \mathrm{s}^{-1}\)
2 \(0.5 \mathrm{rad} \mathrm{s}^{-1}\)
3 \(2 \pi \mathrm{rad} \mathrm{s}^{-1}\)
4 \(0.5 \pi \mathrm{rad} \mathrm{s}^{-1}\)
Rotational Motion

149859 A rotating wheel changes angular speed from \(1800 \mathrm{rpm}\) to \(3000 \mathrm{rpm}\) in 20s. What is the angular acceleration assuming to be uniform?

1 \(60 \pi \mathrm{rad} \mathrm{s}^{-2}\)
2 \(90 \pi \mathrm{rad} \mathrm{s}^{-2}\)
3 \(2 \pi \mathrm{rad} \mathrm{s}^{-2}\)
4 \(40 \pi \mathrm{rad} \mathrm{s}^{-2}\)
Rotational Motion

149860 When a ceiling fan is switched off, its angular velocity reduces by \(50 \%\) while it makes 36 rotations. How many more rotation will it make before coming to rest? (Assume uniform angular retardation):

1 36
2 48
3 18
4 12
Rotational Motion

149861 How much revolution does the engine make during the time when a motor wheel with angular speed is increased from \(720 \mathrm{rpm}\) to \(2820 \mathrm{rpm}\) in 14 seconds?

1 354
2 490
3 413
4 620
Rotational Motion

149856 Three particles \(A, B, C\) are situated at the vertices of an equilateral triangle \(A B C\) of side \(d\) at \(\mathbf{t}=0\). Each of the particles moves with constant speed \(v\). A always has its velocity along \(A B, B\) along \(B C\) and \(C\) along \(C A\). The time the particles meet each other is

1 \(\mathrm{d} /(3 \mathrm{v})\)
2 \(2 \mathrm{~d} /(3 \mathrm{v})\)
3 \(3 \mathrm{~d} /(2 \mathrm{v})\)
4 \(d / v\)
Rotational Motion

149857 A particle executing SHM has a maximum speed of \(0.5 \mathrm{~ms}^{-1}\) and maximum acceleration of \(1.0 \mathrm{~ms}\) . The angular frequency of oscillation is:

1 \(2 \mathrm{rad} \mathrm{s}^{-1}\)
2 \(0.5 \mathrm{rad} \mathrm{s}^{-1}\)
3 \(2 \pi \mathrm{rad} \mathrm{s}^{-1}\)
4 \(0.5 \pi \mathrm{rad} \mathrm{s}^{-1}\)
Rotational Motion

149859 A rotating wheel changes angular speed from \(1800 \mathrm{rpm}\) to \(3000 \mathrm{rpm}\) in 20s. What is the angular acceleration assuming to be uniform?

1 \(60 \pi \mathrm{rad} \mathrm{s}^{-2}\)
2 \(90 \pi \mathrm{rad} \mathrm{s}^{-2}\)
3 \(2 \pi \mathrm{rad} \mathrm{s}^{-2}\)
4 \(40 \pi \mathrm{rad} \mathrm{s}^{-2}\)
Rotational Motion

149860 When a ceiling fan is switched off, its angular velocity reduces by \(50 \%\) while it makes 36 rotations. How many more rotation will it make before coming to rest? (Assume uniform angular retardation):

1 36
2 48
3 18
4 12
Rotational Motion

149861 How much revolution does the engine make during the time when a motor wheel with angular speed is increased from \(720 \mathrm{rpm}\) to \(2820 \mathrm{rpm}\) in 14 seconds?

1 354
2 490
3 413
4 620
Rotational Motion

149856 Three particles \(A, B, C\) are situated at the vertices of an equilateral triangle \(A B C\) of side \(d\) at \(\mathbf{t}=0\). Each of the particles moves with constant speed \(v\). A always has its velocity along \(A B, B\) along \(B C\) and \(C\) along \(C A\). The time the particles meet each other is

1 \(\mathrm{d} /(3 \mathrm{v})\)
2 \(2 \mathrm{~d} /(3 \mathrm{v})\)
3 \(3 \mathrm{~d} /(2 \mathrm{v})\)
4 \(d / v\)
Rotational Motion

149857 A particle executing SHM has a maximum speed of \(0.5 \mathrm{~ms}^{-1}\) and maximum acceleration of \(1.0 \mathrm{~ms}\) . The angular frequency of oscillation is:

1 \(2 \mathrm{rad} \mathrm{s}^{-1}\)
2 \(0.5 \mathrm{rad} \mathrm{s}^{-1}\)
3 \(2 \pi \mathrm{rad} \mathrm{s}^{-1}\)
4 \(0.5 \pi \mathrm{rad} \mathrm{s}^{-1}\)
Rotational Motion

149859 A rotating wheel changes angular speed from \(1800 \mathrm{rpm}\) to \(3000 \mathrm{rpm}\) in 20s. What is the angular acceleration assuming to be uniform?

1 \(60 \pi \mathrm{rad} \mathrm{s}^{-2}\)
2 \(90 \pi \mathrm{rad} \mathrm{s}^{-2}\)
3 \(2 \pi \mathrm{rad} \mathrm{s}^{-2}\)
4 \(40 \pi \mathrm{rad} \mathrm{s}^{-2}\)
Rotational Motion

149860 When a ceiling fan is switched off, its angular velocity reduces by \(50 \%\) while it makes 36 rotations. How many more rotation will it make before coming to rest? (Assume uniform angular retardation):

1 36
2 48
3 18
4 12
Rotational Motion

149861 How much revolution does the engine make during the time when a motor wheel with angular speed is increased from \(720 \mathrm{rpm}\) to \(2820 \mathrm{rpm}\) in 14 seconds?

1 354
2 490
3 413
4 620